My previous group did the rotating-GM turntable for a while until I finally got fed up with it. While all of the players were outgoing and accomplished roleplayers, in my opinion, not all were cut out to be GMs. Yet since many of them had ideas for a game, everyone was taking their turns running games (group of six gamers). There were even one or two who did it simply because they felt obligated to do so. Finally I stood up and said, 'okay, I will run the long-term campaign from now on.' They didn't argue.
I love to play in a good game, and I've been lucky to have been in some great groups with players who can have a good time, and who value a good adventurous story. I think running games for so long has definitely helped my skills at being a player. I'm more outgoing with my characters, I tend to take risks instead of being quiet and playing it safe.
The most important thing I've learned from being a GM is that I'm willing to have my characters suffer in order to advance the plot and the story. If the GM needs for a character to be put in dire straits to make a situation seem more oppressive, give me the shortest straw. I love adversity in games, because rising above it makes it that much more memorable. Not everyone sees it this way, and grumbles heavily when they feel the GM is actively working against them. Yes, it can be overdone ( " You're all unconscious, no saving throw." ), but fortunately I have only had that happen to me once or twice.
On the flip side, my years of playing have taught me what I enjoy in games, and what I should strive for as a GM. I try to take time and pay attention to each character, bringing in their backgrounds and making them integral to the story. When things look bleak and that one character has to step forward because their skills are the only thing that can save the day, that's priceless. Another one that comes to mind is flexibility. There's nothing worse to me than playing a game that is basically a narrow corridor of plot, where you cannot stray from the path. You will go from point A to point B, do not pass Go, do not collect $200.00. If the players want to take a different approach, I'm all for it. I'll eventually steer them back on course, but I respect their free will.
So in essence, I think you do need to walk a mile in each other's shoes. GMing a game may not be everyone's cup of tea, and I can respect that. But I think everyone should give it a shot, and most definitely, everyone should take the role as a player.