The main objection has to do with the fact that its largest part belongs to Asia both geographically and culturally; so does its capital. Another reason is that Turkey is a very poor country. A third reason is that it's not a very democratic country. Some stress its distinct religious and cultural difference with the rest of the EU. Are those enough reasons?
Say, I think Puerto Rico is more American than Turkey is European. Why is it not part of the US? I see no reason why it shouldn't be