You partially answered your own question by admitting you don't know much about the fur trade....the thing about hunting (although I dislike guns with a passion and see the 'sport' as being pathetic and cowardly), the animals are allowed to roam in their natural environment and there is no doubt that a skilled gunsman will make an instant kill. The fur trade isn't necessarily worse than the meat trade (I deplore both) however it does encourage cruelty and even worse, poaching, as well as illegal practices as the industry is far less regulated than the meat industry.
I've personally been to a rabbit fur farm and honestly it made me never want to wear fur again. Because fur is such a prized commodity, the animals aren't allowed to move at all because any damage to the fur will greatly reduce profit. There is no sunshine allowed in. The animals are often fed foods that artificially encourage hair growth and shine even though the animal is nutritionally starved. The teeth and the claws are completely removed to ensure that, again, no damage to can be made to fur. It's absolutely disgusting. Because slaughter of animals for fur isn't as regulated (and it's a difficult skill to master), the skinning and the slaughtering is often done to semi-conscious animals. For those animals that are caught for fur in the wild, the suffering is even worse. Traps are set to catch badgers, tigers, leaopards etc. These animals can often be in a trap for a week, slowly trying to chew their limbs off, dying of starvation.
And then of course you have the cat/dog fur trade in china which actually is passed off as other types of fur to the western market...
Why? So a few rich people can have a coat or two? We don't NEED fur. We're an advanced species and we should be compassionate. I don't see why that's a hard concept to grasp. We aren't primitive, we understand the consequences of our actions, we're self aware and understand suffering so why would we ever encourage it?
And PETA are equally against the meat trade so I don't understand where you got the idea that they're hypocritical o_O
P.s. faux fur is made from synthetic fibres, so if you ever wear polyester, nylon etc it's the same thing