I think the average man's animal max is a alpha grey wolf about his size and or weight. He would probably die after the fight is over, or be severely injured. This is of course if he has any wrestling experience since the only way to effectively defeat a wolf or large dog is to wrestle them. Punching is risky for obvious reasons. Kicking could work but its more about keeping the predator at bay.
I do think that a strong fit man with wrestling experience could probably defeat a cougar, but its hard for me to say that because of those claws. I can see it happening but the amount of damage the man would take would be horrific. You see, you could fight a wolf and not have to worry so much about its claws since its not very effective in fights. Its primary weapon is its mouth. If you wrestle it to the ground and manage to get it in some type of hold, then you are fine. However with a cougar, if you were to wrestle it down, you are going to get sliced up in the process. Even if the cougar were in a submission hold, it wouldn't have to force its way out using strength, but by claws alone. Don't forget its back legs which could disembowel your torso. You would bleed out or wouldn't be able to handle the trauma and shock. Most humans can't take trauma too well unless overcame with adrenaline or on some type of drug.
You jump on a cougar's back (if you're fast enough) and get it in a head lock. It could just slash at your arm. Either you let go and get mauled or put the cougar to sleep (or kill it) and likely have to get your arm amputated. This example was based off of an actual fight between an old man and a leopard. The man strangled it too death, but he had to get his thumb amputated.
A cougar would kill a man more often than not, but if these were circumstances were both of them were fighting head on and using everything they had, I think the cougar would badly injured (the man in desperation may gouge out the cougar's eyes or punch the nose several times, or pull off an ear, or even attack the groin of the cougar or all of the above.) But more likely than not, a cougar will flee from a man if he is willing to fight hard.