I think one thing that makes revolvers SEEM more reliable to some folks is that their mechanism is largely exposed to view; it is reassuring to see the cylinder turning and hammer coming back
It's a bit more basic than that, speaking for myself only: A revolver is a simpler mechanism. Your finger pulls the trigger, and that cycles the action. These are precision tools, but they are simple. The cylinder rotates, putting a cartridge behind the barrel. The hammer pulls back, and falls. There are some different kinds of firing pins, but the hammer causes the pin to hit the primer and bang. In single action, the hammer is cocked and need only be triggered to fall and fire the bullet.
The automatic comes in several flavors with different mechanisms, but
the general idea is:
A magazine is inserted into the pistol until the magazine release button's stop is engaged.
The slide is then pulled back, which cocks the hammer and is then released, and is pushed forward by the recoil spring. A round of ammunition is stripped from the magazine by the breech block and is fed into the barrel's chamber. The next round in the magazine is forced up by the magazine spring.
The trigger is pulled, drawing forward the trigger bar which pivots the safety lever forward which raises the firing pin safety block allowing the firing pin to move. At the same time, the trigger bar pulls forward the sear from the notch on the hammer, releasing the hammer which is pushed forward by the main spring and hammer strut, so that it strikes the rear of the firing pin which hits the primer.
Then, after the round is fired, the force of combustion drives the bullet out of the barrel and forces the empty cartridge case backward, which thrusts the slide to the rear. The safety lever and firing pin safety block are separated activating the firing pin safety block. A protrusion on the top of the trigger bar is forced downward as the slide moves rearward, forcing the trigger bar downward and disengaging it from the safety lever. As the slide travels rearward, it takes the barrel with it, until the barrel is stopped by the locking insert, tilting it down and away from the slide.
And that's shortening the explanation from the linked page. It's very complex, with lots of moving parts and the ejection of the spent cartridge can sometimes fail to escape the port and get caught and the magazine might misfeed and so forth.
As any auto owner can testify, the above process can occur thousands of times without fail, but revolvers are much more simple in design and fail less often because there's simply less to go wrong. I'm a long-time gun owner and shooter, from my youth, and I've never yet had a revolver fail in any way.
Still, for CCW, the .357s are bulky to carry around and the increased firepower an automatic offers combined with a low profile makes something like the S&W Sigma 9mm looking very attractive to me in terms of price and performance and I'm shopping for one now. I'm not bad-mouthing autos. I like them and will soon be laying out cash for one. My nightstand gun is a revolver because the odds of failure are so close to zero.