Okay, is this type of behavior normal? [Fighting over who is the main tank]

A few days ago I formed a group of 4 to run a Heroic on Balmorra [Empire]. Once all 4 people came together, I asked who has any healing abilities and someone answered yes. So that was great because no matter who else we have, as long as we have a healer we should be fine. So because I was a level 18 Juggernaut at the time, I said that I would be the Tank. No less than 10 seconds after that, a level 20 Assassin abruptly said that he should be the Tank. He never explained why, but just took it upon himself to Tank. Maybe because he was a level 20 Assassin and I was a level 18 Juggernaut and he assumed that because he is 2 levels above me, that makes me an inferior tank.

Anways, onto the Heroic, He would start every fight by putting someone in CC and then we all attack the same enemy. He would run around hitting every enemy in the mob trying to draw all of their aggro [minus the one that he has in CC]. So at any given moment, there are like 4 enemies all attacking this person. I saw how his health keeps getting low and how the Healer [who btw wasn't spec'd as a healer but rather as a DPS but had one or two healing ablities] was struggling to keep this guy alive. So considering how I have a taunt, I decided to help this guy out and out of a mob of 4-5 people, I would taunt about 2 of them just to take some of the threat off of him. I mean, technically, I am a tank so I didn't see any wrong in "sharing" with him. He draws about 2 people and I draw about 2 people and because we evened out the threat, our health is always nearly 80% full so the "healer" could use his many DPS attacks on the enemies to get through the mob quicker instead of trying to heal this "superman" Assassin who is always a second or two away from dying before I take some of the threat off of him by taunting. Again, mind you, that our healer was really a Sith Sorceror who was spec'd in the DPS tree, not healing tree, so his healing was VERY minimal so no need to put all the strain on him.

ANYWAYS, about 70% through the Heroic the Assassin mentions in the party chat [he could have just whispered at me] that "Because I want to use taunt, how about I go ahead and tank." I laughed when I heard that and just continued on.

Why would he say something like that? Was this person really upset because I used taunt to HELP HIM out when he was in situations where he was about to be whipped? Again, we really didn't have a true healer so him taking on 5 elites was just stupid, might as well split it up which worked out just fine but apparently, he didn't like that and like a 6 year old kid who is frustrated, he just told me out right that I tank. So for the rest of the heroic, I was drawing 5 guys and the ironic thing was unlike him whos health would constantly drop to around 10% before I bailed him out, my health with 5 guys attacking me NEVER went below 60%

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Sorry for the wall of text but this is my first MMO. I plan on being a Tank with my Juggernaut in end game content and when I play my Jedi Consular, I plan on being a Healer in end game content. I just want to know if this is something that I should expect to see a lot, people fighting over WHO is the main Tank or WHO is the main healer and what not? Personally, it is just a game and if I am reduced to a off Tank or off healer, then I am fine, as long as we as a group whether it be Heroic, Flashpoint, or Operation accomplish our goals. However based on what I previously experienced, people get really up tight about not wanting anyone to do their job and such.

Is this normal?

I think the biggest issue is a lack of communication. In my opinion the best course of action would have been (after seeing the problems with the healer keeping up) to say, "Hey man, it looks like you're taking a little too much damage for the healer to keep up. Mind if I off-tank and we split the mobs to even out the damage? It'd make things easier overall, and might even let the healer dps a bit."

This x100. I totally understand the tank's frustration (having spent a lot of time as a tank in other games). Without communication and with his focus on trying to round up 4-5 mobs, it would be frustrating to see that one constantly peels off, as the proper reaction for the tank would be to get the mob back under control.. which usually means finding the mob in the pack, burning cooldowns/taunts that you may have wanted to use at other times in the fight, etc.

For all the tank knows, maybe you erroneously thought that taunt was a dps ability and you've worked it into your rotation. Without telling him what you are doing there is no way he knows why you are taunting mobs off him (other than to make his job harder/frustrate him).