The short answer is: in more ways than I can cover in a single section or even a single article. But I am sure going to try! WoW is a common example, but the same problems crop up in other similar MMOs: Lord of the Rings Online, Age of Conan, and others that follow the same quest obsession.
I am going to start right off with the main reason quest heavy MMOs go wrong. Quest heavy advancement is actually a disincentive to grouping. Forced grouping is bad, but anti-grouping is even worse. If people would LIKE to group with people, but the game discourages it, that is an absolutely terrible condition. To whatever degree questing pretties up the grinding process to make it seem less tedium, passing the time chatting with actual people is a million times better.
How does quest heavy advancement discourage grouping? Because it is virtually impossible for people to stay synced up as far as quest progress. When I play MMOs with my wife, it is hard enough for us to keep two characters in sync. Imagine friends who don't live together. Imagine more than 2 people? Unless you all agree to never play certain characters except when everyone is together, you can't stay on track. This means some people always have to be caught up, others are way ahead, and there are always people redoing content and feeling like they are wasting time.
It is even worse for pick up groups, because the odds of being on the same step for more than 1 or 2 quests in a row are extremely slim. So if you happen to find someone who needs to do the same objective, you usually group up, beat that one quest, and then part ways. That usually follows from a brief discussion like this:
Player 1: Have you done Find the 12 Foozles yet?
Player 2: Yeah, already did that. Have you done Rescue Princess Esmerelda?
Player 1: I'm on step 8 of that.
Player 2: Oh, I'm only on step 2. Want to help me catch up?
Player 1: (unless he is extremely charitable) Well.... (uncomfortable), I really need to finish <something for some reason or other>.
Player 2: Ok. Take care then. Thanks for the group.
Player 1: See ya!
(Keep reading... there is much more!)