The thing I think people fail to understand is that you really can end up getting the same results regardless of which mode you use, they just attack the problem from different angles.
P mode starts with what it thinks the best combination of shutter speed and aperture are, and you can then adjust from there. So, for example when you know you're just going to want relatively straightforward exposures, it may be easier (or in terms that won't offend experienced photographers 'a more efficient workflow') to start with P and adjust as necessary. So, you see what P gives you, and you decide you want a bit more shallow DoF, then just adjust, P will fix the shutter speed for you, or you can change the ISO. I've began experimenting with P when doing street photography sometimes. In street, sometimes the moment is on you before you have a chance to get everything set up. If you see a shot coming and you can anticipate it, sure, then switch to manual or A or something. But having your camera ready to go with a relatively high ISO and in P mode guarantees that if something comes on you in a hurry, you get the moment. Which is much more important than some ephemeral badge of honor of shooting it in manual.
A (Av) mode attacks the problem by again giving you what it considers a proper exposure, but holding the aperture constant. As aperture is usually more important for artistic elements in photography, this is often something photographers do want control over. You can then decide you want a darker or brighter exposure than the camera thinks by using exposure compensation. Really, if you use EC heavily, A or S mode are literally the same exact thing as shooting in manual, just that the camera changes it's setting first and then you adjust, instead of having to adjust whenever the scene changes. For some shooting scenarios A is more efficient, in some M is more efficient. One isn't more of a 'true photographer' skill than the other. Just different approaches to the same problem.
S (Tv) is pretty much the exact same thing as A, except it gets used a bit less, because usually shutter speed doesn't change the artistic feel of the photo, unless you're using flash or shooting fast moving subjects.
M is sort of obvious in that you need to decide if the settings need to be changed.
The funniest thing in the world to me are the people who "always shoot in M, because I'm not an amateur", but essentially just shoot to center their light meter every time. Don't they realize that if you shoot that way, you're essentially shooting in A mode, but forcing yourself to turn the command dial instead of letting the camera do it? If you're going to shoot in M, then the whole point is ignoring what the in camera light meter is reading to some extent. The whole point of shooting in M is to use the light meter as a tool, but not a thing that tells you how to shoot. Yet some people will center the in camera light meter on literally every single shot they shoot in M. That drives me more crazy than the people who shoot in full auto.