Should I stop hanging out with him?

I am having trouble with my friend who I hang out with for sometime now. We hung out just as friends, but we've been to the movies, dinner/ lunch etc for a couple of times. Last Saturday, we have decided to hang out, but changed a couple of our plans due to an event we attended, but left in 10 minutes. My parents are involved because they think I like him more than just a friend. This was not my fault though, he is my dad's friend & I am just trying to give him some face. What should I do? I need to stop hanging out with him I think.