Because it's historically part of Europe and has been on the path to joining  the EU since very, very early on. Because it's a huge market that wants to join. Because it's a secular democratic state that wants to join. Same reasons that apply to any other candidate country.

The reason for not allowing Turkey in? We don't like dirty Turks.

The poverty argument applies to several countries that have already joined. The religion one shouldn't even be relevant. The cultural one is total bollox: much of Turkish culture is shared with the other states in the region and is heavily influenced by and influenced Europe. Their organs of state are derived from the French, their civil code from the Swiss and their  alphabet is Roman. Turkey is Muslim in the sense that France is Catholic.