You're not obligated to, but as you can see not adding her is creating more problems than it is solving. This is his wedding too and if he wants his sister as a part of it she should be, even if she is standing on his side.
My husband and I picked our bridal party together. Some of the bridesmaids were his picks and some of the groomsmen and an usher were mine. He's very close to both his sister and sister-in-law and he wanted them both in the wedding and since it was his wedding too, they were. He also has a niece he's very close to and she was a jr bridesmaid. 2 of his groomsmen were my brothers and one of the ushers was my cousin. I didn't know his sister or sister-in-law that well at the time, but I have a really good relationship with both of them now. I get along really well with my in-laws and I really never thought of not having his sister.
I've been sister of the groom twice. I'm close to both of my brothers. I was in one of their weddings but not the other. The one I wasn't in, he regretted not having me the day of the wedding when well I was the only sibling not in in the wedding between them, but mostly when his friends and some family members asked him why I wasn't.
"I'm not having her because she didn't have me" is quite petty. It's the "adult" equivalent to "you're not playing the game the way I wanted you to, so I'm taking my ball and going home".
In married life you need to work on compromising and well in some cases learn to pick your battles. This really isn't a battle worth having.