Here is one of the arguments that convinced me, starting from these two (subjective) ethical principles:
1: Being alive is better than being dead.
2: Being free is better than not being free.
I do not need to eat animals to survive (nor to live). Thus, in accordance with my personal ethics, I try my best to let animals alive rather than dead.
I also do not need any products from their exploitation (eggs, milk, etc.) to survive (nor to live). Thus I try my best to let animals free rather than exploited.