I don't want to walk with my girlfriend for graduation
Are you worried that walking with her might hurt your reputation?
Yes, I think of it as humiliating myself. There's no way I am ashamed of dating her.
If you are ashamed of your girlfriend then you should break up with her. If she finds out, she would be hurt and wonder why.
But I'm nowhere near that. I am ashamed sometimes, but I also care about her and we have a good time together.
If you can get past being ashamed that is great, if you break up with her, that is also acceptable, but it is wrong to stay in a relationship where you do not respect her enough to not be embarrassed.   You need to make a choice one way or the other.