For one man to force another man to do anything through male peer pressure in that special trademark way.
This includes verbally degrading their ability to do anything or stressing a scoff full of testosterone and disbelief to make the person feel inept.
Usually ends up including "do you want me to do it FOR you?", and typically ending up with the situation in question turning out poorly even though the person in question succumbed to the mantagonizing.
AJ: I don't think I'm going to fit into this parking spot...
Brett: Oh come on, you've got plenty of room.
*AJ starts backing the van up*
Brett: Are you serious right now? Do you want me to park the van for you?
AJ: Fine, I'll park here.
*AJ parks successfully*
Brett: Now we've barely got any room to get out. Whatever...
Dev: That was funny.
Andy: Chyep. Is mantagonize a word? If not, I just coined that because that just happened.