You might as well ask the same question in England: why do people still use Kwik-Fit? I ask because of all the people I know who've used Jiffy Lube here in the US, and Kwik-Fit in England, only one has anything good to say about them. The rest are horror stories ranging from the mildly funny to the litigious. For example one of my wife's friends recently went to a Jiffy Lube for one of their "signature" oil changes. The next day, her SUV was parked in our drive and I commented that it was leaking oil. The colour drained from her boyfriend's face as she said "Oh - I took it to Jiffy Lube yesterday". After some not especially complicated diagnosis, it turned out they never bothered to tighten the oil filter when they put it back on, so it had been spewing oil all over the inside of her engine compartment.
This is certainly not the first time I've heard of, or directly experienced this level of service from these places. Apart from anything else there's the up-sell scam they all run. You know the one - where everything was fine when you took the car in, but after the oil change it now miraculously needs new wiper blades or CV boots. When we lived in England, I even experienced one of these places that cut a friend's brake lines so that he couldn't leave the shop without paying to have them all re-done. The litigation on that one found them wholly responsible because they were caught doing it on their own surveillance cameras.
Countless news programs have exposed these places for everything from scamming customers by charging for work and not doing it, to deliberate sabotage, to just making stuff up. Their staff are generally clueless too. A colleague of mine suffered from a catalytic converter theft a couple of years ago. He trailered his truck to the nearest one-stop-shop and their first question was "are you sure it had a catalytic converter in the first place?" followed by "are you sure it was on there when you drove home last night?". (in case you're not mechanically inclined, every car has had a cat for decades, and most modern cars simply won't drive with a chunk of the exhaust missing because of the lack of back-pressure. Oh and the noise would have given it away, obviously).
I just can't fathom why anyone still uses these places.