This isn't limited to athletics. When most people talk about having gone to college, they'll usually say "When I was in school..." or some variation such as that. But I've noticed Notre Dame graduates tend to say "When I was at Notre Dame..." I'm sure there are other schools where they do that as well.
Some people just want you to know they're better than you.
Ha ha! Several years ago, I was making conversation with a new colleague. I asked her where she went to school. She looked at me, looked down, looked back at me and said " oh, does it matter? I don't like to let my school define me". Now, growing up in MA, I had heard of the elusive Harvard grad, but had yet to meet one in the wild. I couldn't believe what was happening. I took a chance and said, " you went to Harvard". She laughed and said that Harvard actually tells them to say that! So sometimes the school itself is to blame for silly things alumnae say