I teased my friend by asking him embarrassing questions.
What do you mean by embarrassing?
Questions he wouldn't want to answer but by not answering it made it seem like the answer was yes.
Pushing your friends to embarrass themselves may seem funny to you, but you don't know how they are reacting to the incident. Bad memories can last a long time and hurt feelings down the line. Apologize to your friend for pushing them.
Why do I have to apologize when he embarrassed himself?
You shouldn't let a friend embarrass themselves in the first place, and especially not instigate it. How would you feel if they did the same thing to you or even worse, if those questions brought up something painful in their memories? Try to consider those things before oyu tease someone like that.