I'm thinking of encouraging my girlfriend's art when I don't think it's that good
Why are you not being more honest with her?
I'm giving her false complements so she will think I have the taste of an art critic
Just because you want your gf to think that you are accomplished about art evaluation, doesn't make it right to lie to her about her art talents. Tell the truth even if it doesn't get you what you think you want.
I'm going to push her towards the art career anyways if I want to.
I think that it is good to encourage her but being honest is just as important and the most loving thing you can do -- not as an art critic, but from your perspective.