Youth Division

What context are you talking about here? What is a youth division?

The members of our temple are classified as follows:
The children are grouped under Children's Division, the adults, under Men's Division and Women's Division.
The youths are under the Youth group.

My question is how should the group of youths be called?

Youth Division, Youth's Division or Youths' Division.

Both Youths' Division and Youth Division are correct. In the first, Youths is a plural noun, in the second it is an adjective. Given how your other groups are named, I would go for Youths' Division to be consistent.

I was taught that it should be "Youth Division". Does it mean that I was taught wrongly?

No; it's not wrong. As engineer pointed out, consistency with the other names might suggest 'Youths' Division'. Personally, however, I prefer Youth Division. There's no difficulty with apostrophe placement, for one thing. And making the plural noun possessive ends up with a difficult cluster of consonants to pronounce: the -ths' combined with the d is hard to enunciate.