AITA for telling my sister nobody cares what college she went to?

I (35M) have a sister (28F). My sister who went to Dartmouth college and got a degree from there. I’m glad she did, but she’s always bragging about it. No matter what conversation we’re having, somehow she always has to slide in that she went to Dartmouth. So much so that she has put me down for my degree since I went to a college with an 80% acceptance rate. I’ve never seen the hype in different schools honestly. It’s all the same piece of paper.

Well, our parents invited us and our other siblings over for dinner. Afterwards, me and my brother were literally having a conversation about our finances. My sister of course had to jump in with the whole “I went to Dartmouth” nonsense. I told her that nobody cares that she went to Dartmouth. Nobody cares where your degree is from they just care if you have a degree. I told her to please stop bragging about having gone to an Ivy League school, because it doesn’t matter at all. She then looked offended. She said “it’s not my fault you went to a mediocre school, so stop being jealous” I rolled my eyes and turned back to continue talking with my brother.

Later my sister texted me saying what I said was an AH move and I owe her an apology. AITA?