As I stated in my opening comment, I have played healer (WHM) up until around lv 49-50. I couldn't get into it. But I do agree with this. Playing a healer does give you a good perspective on how runs go usually and some of the difficulties you can deal with as a healer. And yes, it does improve tanking AND playing as a DPS.
Someone else mentioned the same thing in this thread. And yes, while I agree that it is annoying, as a tank grabbing enmity is extremely easy using your tank stance and using the tools provided to you (provoke, AoEs, long range enmity attack) A few AoE spams will gain enmity very quickly. Provoke puts you at the top of the threat list instantly but you have to follow it up with an attack. (Usually your long range skill) I was always taught that no one makes a move before the tank. DPS and Healers should be polite and wait for them to pull before doing anything. I also know that some people are new or just impatient...which can't be avoided.
Sounds like you've just had bad experiences with a small percentage of the playerbase. Honestly, I've only encountered this at the most 2-3 times in my 5 years of playing this game as a tank and I felt the same way. I wanted to stop tanking but instead I chose to work on becoming a better tank so that that situation would never happen again. No one plays perfectly. Maybe check out some tank guides and work on making yourself better. That's what I did regardless of if I was doing well or if that person was just being a jerk. Ask people questions who DO main tank.
I've also heard from some of my healer friends that healing gets easier as you level. So easy that some of their spells heal for absurd amounts especially in dungeons. It's not a big deal if you aren't constantly topped off and "overhealing" is a thing. It goes back to the "trust you healer" thing I mentioned before. It's like yeah, your health dropped but did you die though? No? Then you're fine. Keep it moving. lol