Should we call it "birthday" or "anniversary" ?

I brought that question, since I can't decide whether it's a birthday .. or merely an anniversary. Here's the situation;

We were some highschool grads, continued our study to this college where we all met. And it's been a habit to celebrate the day we first met (Sept 17th) every year! So, what is it? A birthday or an anniversary?

Birthday pros:

Hey, birthday is only for something that is related to "the birth of a living thing" and I guess friendship don't fall to the category. But, we're all feel like the arrival was the birth of a new group of generation.