When did this trend start? And why? I mean, I can see if tiger skin were popular, cause hey, you can tell people you killed it with your bare hands. But a cow? Not really that scary.
When did people first equate black leather = being a badass?
I would say the most likely is that bikers wear it, the motorcycle type that is. They of course started wearing it because it protects fairly well and is comfortable to ride in. The rise of biker gangs, which most people automatically equate with the Hells Angels who are considered quite badass probably helped the link between wearing leather = ultra bad.
Let’s not forget WWI fighting aces.
Yeah, a big part of it is supposed function. Leather is basically armour.
Tiger-skin isn’t going to help much if you’re sliding on the pavement at sixty mph, and the idea is that it’s cool that you’re prepared for that.
On the other hand, leather doesn’t necessarily equal cool – I feel like a big geek when I wear my beat up old leather jacket. That’s probably because I am a geek, and I ride the bus.
I still feel cooler than people who wear leather and think it projects “bad-ass,” though. 
Arthur Fonzarelli
Though before my time, it seems like it must have been Fonzie.
Later, the Terminator.
Bah, forgot about that. And I’m from a military family!
Young punks! James Dean and Elvis Presley
IIRC, originally the “gangs” were composed of recently returned verterns of WWII and many wore their old bomber jackets and field jackets. I seem to recall they were brown and OD respectively.
As stated before, it acts a defence against road-rash and the cold and rain. Same can be said for blue jeans and boots that also are popular. The black is popular, imo, due to the ever-present grease and oil when dealing with old bikes.
Many aspects of the clothing are functional. The leather for rain/cold, black to hide the grease, the denim jeans to also protect the hide, the boots to stay on your feet in the event of a side-slide, the chain wallet because if it falls out of your pocket in the car, it will be there when you stop. Not so on a bike. Sunglasses are your windshield.
Young punk. You mean Marlon Brando. The WIld Ones was two years before Rebel Without a Cause. That’s the movie that started it all off.
And Fonzie? Time to weep. Other than Kelso on That 70s Show, who in America ever imitated Fonzie?
And these two…
Every frat guy that pops his collar up on his Hollister shirt is imitating the Fonz look.
Or maybe they’re imitating the people that Fonzie imitated when he did that.
The Fonzie character may have originated “Heyyyy…,” but I think you’ll find everything in his appearance copied earlier sources. Of course, some of you young punks may not know those earlier sources, and are actually imitating the Fonz. 
That’s not a leather jacket James Dean is wearing in Rebel Without a Cause. It’s a red Windbreaker jacket. Dean never wore a leather jacket in any of his movies, although he was a motorcyclist in real life.
The Gestapo certainly helped the leather = bad ass cause.
Gregory Peck. John Wayne, and Cary Grant (prewar, too) beat out Brando. There are probably others.
It’s clear that WWII bomber jackets were the beginning of the style. Bikers took to them because they protected against the wind, and kept up the image. Brando was only using copying their style – The Wild One was based on a real incident, and Life Magazine had photos of the bikers involved, all wearing bomber jackets.
I’d say James Dean’s T-shirt and windbreaker was as influential in its time than Brando’s leather jacket, though – maybe even more so.
I had a WWI pilot’s jacket. It was lined with sheepskin and came down to about the bottom of the butt. It was cool in its own way, but pretty bulky and too long to be comfortable on a motorcycle. I would agree with RealityChuck that the WWII jackets are the direct antecedent of the biker/badass/cool image.
There’s imitation, and there’s fads, and there’s cool.
Some black leather jackets existed earlier. Perhaps airline daredevils wore them. Bomber pilots didn’t wear black leather, but their look could be imitated. Bikers had an image but few wanted to imitate them.
Fad and imitation and cool didn’t really all come together into a package until Brando. That’s when the look became cool. Before that it was just a look.
Even Kelso was trying to imitate Brando, and got upset every time people called him the Fonz. 
I imitated Fonzie. Of course I was nine.