It shouldn't matter to you what choices your friend makes.
If she is sneering at you for your choices, or slagging you off for them, or judging you..they would all be very valid reasons to end the friendship.
But if she is simply making a personal choice for her children, then that is none of your business. She had a pov, a theory. When it came to it, when it was a reality, her kids in front of her, what should she do, what should she do..?? she made a different choice. Fair enough. That's up to her.
Before I had kids, I swore they'd never have a dummy. That people who gave their kids dummies were neglectful and using them to shut the kids up . I made all sorts of judgements (on that and many things). I think I lasted a week before I went and bought a set! When I went into hospital to deliver ds2, I took a pack with me!
Do you see what I am saying? What you think about something when you are not in a situation where it's relevent can be VERY different from what you think is best when you are facing it.
She's not sending her kids to private school to get at you, or to send a message to you, or for any reason in any way connected with you. It's about her choice for her kids, not about you and you shouldn't be trying to hijack it.
Do you like her? Does she like you?
You don't have to only ever have friends that are exactly like you in every way, hold the same opinions on everything, grew up next door and have the same bank balance. It is extremely enriching to have friends from all backgrounds, with opinions that differ from and which challenge yours. As long as you respect each other and each others right to make choices that are different from yours, and there are no aspects of them that are unforgivable or repugnant to you (eg for me, such a trait would be racism or spitefulness).