The closest I have been to a grenade is from the TV set and I find it really dangerous because once the pin is pulled, everywhere goes boom.
I have seen in movies how soldiers pick it up and throw it, I always thought they were overdoing things but it looks like it's very possible since there is always a little time between pulling the pin and the explosion.
Assuming it was thrown and in the air for a couple seconds it would explode in your face before you had the chance to pick it up and throw it back...You might have missed this part of the posts about the four second fuse.