Being "brought up" Catholic is a pro.cess. Maybe you already know but going to church in Sundays and being brought up Catholic are two wildly different things. To be brought up Catholic you
This may or may not be something OP is against.
Take catechism classes when they are young so they can't get their first communion.
Take communion on Sundays. Something OP can't do because he's not Catholic. Doesn't seem like a big deal, but as a non-Catholic who dated a Catholic, it makes you feel kind of awkward.
Taking confirmation classes and being confirmed.
This usually happens when they are teens. They take classes and go through a process to make them an official member of the religion.
Depending on how devout the OPs SO is this could also require Midnight Mass, making their child go to confession, etc.
If you aren't religious, bringing your child up Catholic is very awkward because it's super ritualistic.