I'm going to skip my brother's birthday
Why are you going to skip your brother's birthday?
I just don't feel like his birthday is that big of a deal.
It can be tedious to attend a birthday party, but when the party is for a close family member then you should attend. If you don't attend your brother's birthday party, he may think that you don't care about him.
I just don't care about him or his birthday.
I just don't think you should miss his birthday entirely. You should at least go make an appearance.