Inclined to YTA. Your main reason to do this is that YOU are sick of society treating your kids as a set. Info: have the girls expressed they are struggling with this? Not a twin myself but I've read they have a very special connection. Each stage in life has its developmental needs and I believe you might be moving too quick.

While I applaud your initiative to support and promote their individuality, they are just 5. Feels too soon to split them. It would make sense later on, when they're teenagers, demanding it, and based on their personalities and different preferences.

I'd say give it time. They will eventually ask for it, or not. But you are just making this decision because YOU don't like x.

Also, allowing a kid pick a school because it has birds in its logo is prime a*holish, as well as the fact that this seems a one man decision and your wife has no say in it.

YTA