I've backpacked a lot in the desert southwest and seen lion tracks many times. And bear tracks. And rattlesnakes
So what?
People in this country in far more danger from automobiles, junk food diets, and criminals than wildlife.
Not when hiking in mountain lion country.
My company required that I get bear training and be accompanied by an armed bear guard when going to remote parts of Alaska on company business. Guess they should have talked to you first.
"So what?"
So... keep backpacking and enjoy nature. I don't see anyone here saying that you shouldn't.
Also be aware that cougars/mountain lions/panthers are protected by our government.
If you carry a firearm and if, on one of your backpacking trips you happen to spot a mountain lion/cougar/puma in the scope of your firearm and if the animal is close to you, it might be good for you to know that our laws prohibit you from shooting the mountain lion until you, or any companion backpackers would be considered to be "officially in danger."
The problem of course is that you or any companion backpackers might not be lucky enough to spot the animal until it's upon you.
They are carnivores, they eat meat.