the sea of wannabes

You don't need a university degree to do personal training well. You do need one to help high-risk people, those recovering from strokes and so on. But this is a tiny minority of the gym population. The best personal trainers have the following,

• Have hired a trainer themselves. They actually believe in and value PT.
• Have a background in movement - doesn't have to be weights, could be gymnastics, tennis, a martial art, etc - in which they've done moderately well over 2+ years. Having moved, they are used to watching movement, and thus understand movement better. This is the beginning of the "coaching eye."
• Have set modestly ambitious physical training goals taking 6+ months to achieve, and achieved them, eg a young woman deadlifting 100kg, a guy running 5km in under 20', either going from healthy bodyfat to sixpack abs, got a black belt in a martial art, rehabilitated an injury requiring surgery, etc. They've done something physically challenging and in which they'll have fallen back along the way (as opposed to the easy newbie gains).
• Some general life experience - other jobs they've been successful at, been married, had children, screwed a few things up, etc. This gives them perspective and empathy which helps them get and keep clients, and get them results.
• Enthusiasm for deeper or broader knowledge of health and fitness, ie they keep studying, including trying out things they think are stupid, so they can have an informed opinion on them. This is quite simply professional development, ie getting better at your job.

Not everyone will have them all, the best will though, and most can be developed over time. There are other things that matter but this will do for a blog post which few will read. 

Think of the trainers you know and ask yourself which of these traits they display. In the US, the number of personal training clients is estimated at 6.4 million; 51.4 million are gym members and 12% or 6.1 million use PT services. That's less than one client per trainer. In Australia, it's estimated that we have twice as many PTs as IT professionals entering the workforce every year. Evidently there are rather a lot of unsuccessful trainers out there. Now consider the above list again and see if you can connect the dots. 

It's easy to get the title "personal trainer". It's not easy to get a job and be good at it.

Why lift?

The question, "why lift?" is answered by doing it seriously for 6 months or so. Strength is like education, you don't realise its importance until you have it, and people who are too lazy to get it will come up with all sorts of elaborate arguments about why it doesn't matter to them. 

• "But I don't want to bulk up." I'd believe this woman if I saw her smashing herself with cardio, but she's walking on the treadmill at 4km an hour reading Woman's Day. She's just lazy. 
• "I get enough leg work playing soccer." I'd believe this guy if he were going hard on upper-body, but he's half-benching 60kg and doing one million curls with layback. He's lazy. 
• "I just need to work on my core." This person isn't doing three minute planks, either. The purpose of your "core" (which we used to call "the waist" before it got trendy) is to keep you upright. Is it harder to stay upright with a big-arsed weight on your back? Then you are working your "core" while squatting. They're lazy. 
• "I have a bad back, and bad knees." This is why you must lift, just starting easier and progressing more slowly than someone with no problems. That you don't do it means you're lazy. 

Cardio is important for good health, beyond a certain level it's not helpful. I know many people who ran for many years, and looking back said it was a waste of time. I know nobody was has lifted for many years and said it was a waste of time.

This is the difficult part about selling training, whether by "selling" we mean signing people up for PT, or simply getting someone to train themselves: you don't realise its true value until you've done it for several weeks at least. You lift because lazy is useless, and stronger is better. 

teach correct movement

Just because you don't know how to coach a movement doesn't mean the person can't do it.

Nowadays we have an entire industry created by people who confuse their inability to coach a movement with the person having some mobility or injury issues which can only be fixed by elaborate "activation" exercises and the like, completed of course with lots of pseudoscientific jargon. 

Of course, "shove your knees out" is less exciting than a book full of mobility exercises.

A personal trainer's job is to teach correct movement. If you cannot get a healthy adult under 50 to an unloaded below parallel squat in ten minutes, and if after six months you have that person deadlifting 30kg, you're incompetent.