When do you think hunting is most dangerous?
I believe you mean how does hunting turn dangerous in "The Most Dangerous Game". Basically, boredom and a desire to remain superior is what leads Zaroff to turn to humans who offer cunning and skill that animals never could. Therefore, a sport becomes a murderous chase for humans.
Your question is a bit vague. Are you referring to the story or to hunting in general. In terms of the story, hunting becomes dangerous for Zaroff when he loses the thrill in hunting animals and lets his blood-lust drive him to hunting humans.
It's not the hunting that is the most dangerous it's the game that is being hunted. Zaroff is bored of hunting animals so he captures humans and hunts them on his island called "Shipwreck Island" (but nobody knows about his island.) Zaroff wants the hunt to be as difficult as it could possibly be so he provides his hunt with the most difficult shoes you could track and a knife.