Why does Israel continues to build settlements in West Bank?

Land theft. Before 1948 Jewish immigrants owned no more than 7% of lands in whole Palestine and only 1% in what is now occupied Palestinian territory (Survey of Palestine). Today, illegal Israeli settlers control about 42% of lands in the ccupied territories - I am not talking about the build up area only (B'tsalem). The settlements aim to squeeze the remaining Palestinian population out and to create more Jewish majority areas that Israel could annex in future.

The settlements are illegal, there is no question about that. The International Court of Justice ruled in 2004 that settlements are illegal and that their constitute a breach of Geneva Convention whether they belong to sovereign country or not! UN Security Council Resolution 446 also says that settlements are illegal and so does the entire international community. Our Israeli friends here like to claim that settlements are legal but when you ask them for source (or to refute the sources that say they are illegal) they can't. Israel acquired these territories through war which it started by a SURPRISE attack on Egypt after SIXTEEN years of planning (yet somehow Israeli apologists still insist that Arabs started the war) therefore Israel can't claim ownership there. The medieval age of conquest and colonization is over this is the 21'st century.

The settlements constitute an obstacle to peace because they prevent the establishment of a viable sovereign Palestinian state. Would Israelis accept Palestinian enclaves and roads to cut through Israel?

Finally, the settlements are inhumane and violate the basic rights of the native population like the right to travel (Palestinians are not allowed anywhere near the settlements or to use its roads), protection from settler's violence and land theft (which occurs under IDF protection), equal access to water (according to the UN, French and Palestinian reports illegal settlers receive more water than the native population). About a third of these settlements were built on private Palestinian lamd (B'tsalem).

Israel continues to build homes,villages and towns in Judea and Shomron because these are built on areas of the Jewish Homeland as per unanimous decision of the League of Nations,San Remo,1922.
This is in accordance with International Law.
West Bank is a term used by the Kingdom of Jordan when they illegally occupied and annexed Judea,Shomron and Jerusalem which are all part of the Land of Israel.

To Arabs who still regard Andalusia(Spain to the rest of the world) as still belonging to Greater Arabia,even the small Jewish State,as an affront to them and a deterrent to peace.

The Hebrew Nation was living in Israel 2,000 years before the Muslim invasion,and it's descendants have turned it into an oasis of peace and prosperity once more,to be enjoyed by all it's citizens- Jews,Muslims Christians Druze and every one else.

The question sounds as if the land in question belongs to some other state e.g., Palsetine. It does not. International law is clear on that. The West Bank and Gaza are not part of Israel, AND they are not part of any other state either. The land is in legal limbo until and unless all relevant parties peacefully negotiate final status borders. This is also the meaning of UN SC Res 242.
Depending on who you ask, the settlements are built on land that is as much as 100% or as low as 60% Jewish owned private property or Government owned property. Jews lived in the West Bank and Gaza UNTIL 1948, when Jordan seized it (along with Jerusalem) and ethnically cleansed all the Jews from all those areas and took their property. When settlements are built on Arab owned private property, the Arabs can simply file suit and the Israelis will be evicted. This happened just a few months ago. Some settlers did build on private property of Arabs and the courts evicted them.
Israeli presence in Judea and Samaria is significantly different: the possession of the territory continues for many decades, and no one can predict its end, if at all; the territory was conquered from a state (the Kingdom of Jordan) whose sovereignty over the territory has never been firmly legalized, and in the meantime it even renounced its claim of sovereignty; the State of Israel claims sovereign rights to the territory.
It should be emphasized here that in the Mandate (as well as in the Balfour Declaration) only the "civil and religious" rights of the inhabitants of Palestine are mentioned as rendering protection, but there is no mention of the national rights of the Arab people. And concerning the actual implementation of this declaration article 2 of the Mandate says:

The Mandatory shall be responsible for placing the country under such political, administrative and economic conditions as will secure the establishment of the Jewish national home, as laid down in the preamble, and the development of self -governing institutions, and also for safeguarding the civil and religious rights of all the inhabitants of Palestine, irrespective of race and religion.

And in article 6 of the Mandate it says:

The Administration of Palestine, while ensuring that the rights and position of other sections of the population are not prejudiced, shall facilitate Jewish immigration under suitable conditions and shall encourage, in co-operation with the Jewish agency. referred to in Article 4, close settlement by Jews, on the land, including State lands and waste lands not required for public purposes.
Israel implemented a policy that allows the Israelis to live voluntarily in the territory in accordance with laws prescribed by the Israeli government and supervised by the Israeli legal system, while their continued presence is subject to the outcome of the negotiation process.

Answers from pro-colonials to this question explain why the colonization will continue.

Attitude.

The answer to your question is "attitude" - in this case a very negative, dismissive attitude toward the welfare of others who are not part of their identity group.

The entity has no interest in peace. Anything that say about peace is just window dressing. More land, more water more resources and less for others is the primary goal.

And what exactly makes them a deterrent to peace?
Maybe other's objections to them is a deterrent?

Good Question, but unfortunately due to our media, wrong premise.

Israel doesn't build settlements. Israel builds houses in existing settlements. I don't think there has been a settlement built in around 20 years, prior to the Oslo Accords. Most homes are built, naturally, in major cities. I don't know what you think of when you hear settlements, but some of them are quite large. 30,000+ Residents. Most building occurs in these settlements of Maale Adumim, the Gush Etsion Bloc, Modi'in Illit....

Something you need to know about Israel: It's narrow. Really really narrow. One of the biggest reasons why Israel, after being attacked in 1967, had to reign control over the West Bank is that in some parts, Israel was as little as 20 km wide. It wouldn't have taken an invading army very long to split Israel right in half. Not only that, but most of the population is located in the center of the country. Residents of Settlements tend to live there because of low cost of living, which is a big incentive in Israel, and ease of access to the major population centers such as Tel Aviv. If you're curious about the legality of the settlements, let me just tell it to you as a person who has studied quite a bit some of these settlements is that it will give you a headache. A lot of this land is still under the laws established by the Ottoman Turks, nearly 100 years ago. One could argue all day, about settlement X and Y and legal and illegal and get no where. Honestly, it depends who you ask. Ottoman laws were strange, with rules like if a person did not tend land for X amount of years it becomes state land, and things like that. Now that I have established that, I can properly answer your question.

Israel has frozen settlement home building in the past, and it led nowhere. Settlements are a deterrent to peace in the sense that, Palestinian Negotiators are so stubborn that they make settlements a deterrent to peace.

Israel, throughout its relations with the Palestinians, has always been open to negotiations. Any time, anywhere.

Abbas has always stated preconditions. In the past, it was freezing settlements, which as I said before, led nowhere. As of recently, it was releasing terrorists who committed murder against innocent Israelis. Is having this as a precondition a deterrent to peace? Right now, Abbas basically admitted that despite getting his terrorists out of Israeli jails, he is going to sit tight and do nothing for negotiations because of 'Israeli settlement home building.' Abbas knew fully well that Israel would continue to build home in the settlements. As far as I can see, Abbas just wanted to get Palestinian prisoners out of jail so he could appease his people while not doing anything towards peace. You've seen this in the past before, notably in 2000, when Arafat, despite being given a relatively good offer for peace, he didn't even counteroffer. It's not he didn't like the offer; It's that he didn't return one with his own.

The most ridiculous thing that I never see anyone question is why palestinians have preconditions at all. They want a Palestinian State, yes? Shouldn't they be the first ones to want to negotiate? Does it make sense that they want their preconditions satisfied before negotiations begin? Isn't that the entire purpose of negotiations? By having preconditions the Palestinians are cutting themselves off, and if you think about it, it's a smart tactic.

Settlement homes have never prevented peace in the past, and their removal has never guaranteed peace. The first example is when Israel removed homes in the Sinai Peninsula: This was ultimately done successfully and did not hinder a peace resolution with Egypt. The second example is when Israel did remove settlements in Gaza, where around 8,000 Israelis had Greenhouses and business's that contributed more than 30 percent to Gaza's GDP, and their removal and the disengagement led to more rocket attacks and more instability.

To sum it all up, Israel's settlement population numbers 500,000. There is no way in Hell Israel is going to remove 500,000 people from their homes, some of whom have been living their since 1967, because it would make the Palestinian Government Happy.

Some settlement home building a disagree with: I think Israel should do more to ensure that illegal outposts don't spring up and probably limit building to the major settlement blocs, some of which I mentioned earlier. In any Peace Deal, Israel will get these settlements. More than 86 percent of Israelis who live in settlements live on a land area that is less than 5 percent of the West Bank. In any likely peace arrangement, land from areas to the south and north of the West Bank, as well as land surrounding the Gaza Strip will probably be traded for a long lasting peace deal in which Israel will be able to keep the majority of settlements.

Arabs erect illegal housing within Israel and no one cares. Israel develops housing units on its own land and the world freaks out.

dear Abdul,
because the name of the land is JUDEA, not Arabea...
And capitol city of the land is JEWsalem, not ARABsalem.

Because they hate the rest of the world.