You initiate a wheelie (or manual) by shifting your weight back and cranking down on the pedals. The pedaling force pushes the bike forward under you by driving the wheel ; while shifting your weight back rapidly shifts the center of gravity, causing the bike to rotate. You aren’t really pulling with your arms as much as hanging from them.

Same goes for the (arguably more useful) bunny-hop. You don’t really pull up on the bike, you bounce your weight up, and drag the bike along with you