Tanks are not the boss of anyone. It's a mmo, it's played by a community, if you think you are entitled to rule the party you're mistaken. The tank job is to keep the hate of the mobs on him, the easiest way to do that is to get initial enmity, that why you pull them, it don't mean you can decide by yourself how the run will go.
In dungeon tank are not as essential as they think they are. Did with friends most of the latest dungeon with 4dps/4heal/4tank out of boredom, and had no problem getting a clear, every dungeon could pretty much be done with a 4 monkey team anyway.
If you do end game content you understand really fast that tank are not more valuable than any other member of the team, everyone as to get their game together to get a clear, if you play alone or even fight against your own team you're getting nowhere

Sometimes the attitude of the tanks in this game is really sad. (note that it's not only tank, they are everywhere) Once I got Shiva trial on duty as a smn, trying to get my egi on manual I accidently send it on the boss, proceed to explain and apologize asap. Tanks get in an corner and said you pull, you tank. I actually agree with that but maybe mistake happen, and if someone take the time to explain and say he's sorry it's probably really a mistake. Answer of the tank: "I don't care, I'm the tank I get to decide anyway". in the meantime 4 people die get raised and he decide that his ego his satisfied and pull. I tell him it wasn't very mature of him and once again he reply with "yeah but you're just a dps, I'm the tank, what are you gonna do about it?" and here's happened a kinda cool reality check, 4 dps that didn't know each other before proceeded to sheathe their weapon and started cheer on the tank, that suddenly got all quiet, 10min later and dps wondering if Shiva hard had an enrage before her astral party finally wipe and disband. Sure it wasn't very mature either, but it proved that you can't treat people whatever you want just because you're tank. (I tagged again afterward, got Shiva again with the same tank, we talked like human being before the start instead of acting like kids and got a fast clear)

In OP's specific case. Yeah the dps could've been more polite asking a full run, but he could've explained it to him. As him and his friend wanted it quick I'll assume he were more prompt to react with hostility rather than work a way to satistfy everyone.
It was selfish and not very mature on both part. In that case his friend needed a clear, the other 2 wanted the exp, doing the full run was longer but satisfied both side. But rather than sort it out at the start it did go. dps: Xp k bye -> screw this I'm the boss, I am the hero, I am the tank you'll do what I want -> tank proceed to run through selfishly -> dps aggro everything for his gain selfishly -> everyone act like kid and refuse to work together -> party disband -> new "people don't do it like I want to" thread on the forum.
Maybe one side had to show a bit of maturity and this could've been avoided.