UTG sees you pushing from button and sees you are short, he may call with any pair like 66-TT or any 2 over cards thinking he may have a small advantage...

I would wait until i can enter the pot first even if it is just something like 89s if you are entering first I like it better.

that being said, i do not think it is wrong to push and i would not fault that play, just think there is a better spot coming