I'm not his girlfriend....

Some do, some don't. Younger ones tend to get a bit awkward around the subject. 2 months isn't that long if they've just been casually dating. If they haven't actually talked about it then it would be a bit weird if he introduced her as his girlfriend and she was like "wait, what? Since when?" maybe he is trying to keep it neutral because he doesn't know how she feels about it.

Or maybe he just has a different standard of what he views 'seeing someone' and them being a girlfriend. To some 'girlfriend' is a massive step... To others they use it from the first date. I was in the 'seeing each other' stage with my boyfriend for about 3 months before we actually talked about it and decided to be 'official'. You want to make sure it's the right decision before you go throwing the words around.

Obviously, yes, maybe he isn't that keen on her and is stringing her along. However she will never know until she brings it up.

Some do, some don't. Younger ones tend to get a bit awkward around the subject. 2 months isn't that long if they've just been casually dating. If they haven't actually talked about it then it would be a bit weird if he introduced her as his girlfriend and she was like "wait, what? Since when?" maybe he is trying to keep it neutral because he doesn't know how she feels about it.

Or maybe he just has a different standard of what he views 'seeing someone' and them being a girlfriend. To some 'girlfriend' is a massive step... To others they use it from the first date. I was in the 'seeing each other' stage with my boyfriend for about 3 months before we actually talked about it and decided to be 'official'. You want to make sure it's the right decision before you go throwing the words around.

Obviously, yes, maybe he isn't that keen on her and is stringing her along. However she will never know until she brings it up.