I think I love showing off my girlfriend.
Why do you like showing off your girlfriend?
Well my father is always saying I will never have a girlfriend.
While it's good that you're happy with your partner, be careful not to objectify her. The way you talk it sounds like you almost view her as a trophy to show off to people, rather than a person who you are in a loving relationship with.
I wouldn't call it objectifying. Think of it as I just like to have attention.
Well then it's wrong to objectify her just to get attention. You should only show her off because you are proud of her.