What's caused a lot of confusion in the tank community is the expectation brought into this game from other MMOs, be it WoW, Tera, Rift, whatever. There are SOME MMOs that have a DPS focus on the tanks (Aion springs to mind) but in general, a lot of the traditional MMOs allow tanks to focus primarily on their tanking stats and tanking rotation. They might still contribute a lot of DPS naturally, but they'll mostly be looking to make themselves as tough as possible via gearing/talents/playstyle etc.
In order to fully understand the way tanks are expected to play in FFXIV at the top level, you have to ask the question "what causes a tank to die in an MMO?". Two obvious answers which don't really pertain to the argument are "lag/dcs" (which can happen to anyone) and "messing up a mechanic". There's plenty of instakill mechanics in FFXIV raids that will kill someone or the entire raid if you don't move in the right place or pass a debuff over or somesuch, but those arent really relevant here.
What we need to understand is how a tank that is tanking a boss in an MMO can die, assuming they have a healer healing them. Usually an MMO will have encounters that tend to fit into only one or two of these ways, forcing tanks to gear appropriately. Here's the four primary ways an MMO can setup raid bosses to kill tanks:
1 - Constant Incoming Damage. This is the kind of fight where a boss throws so much damage at a tank that even with a healer spam healing them the healer literally cannot keep up with the rate of incoming damage. The tank dies because the incoming damage rate is higher than the heal rate. This is fairly rare, but usually used in gearcheck encounters. Provided that this sort of heavy tank damage is happening for the entire encounter, the way a tank survives is simple: they get as much mitigation as possible. Dodge, Parry, Armor, Block, whatever, along with a huge health pool. It all helps. In addition, the healers probably need to gear up for bigger heals too. Tanking cooldowns will help, but if the damage is constant for an entire fight you'll need to be able to survive outside of cooldowns via raw tank stats.
2 - Healers Out of Mana. This one was fairly common in earlier days of WoW raiding. You basically throw lots of damage at the tank, but it's fairly easy to heal. However, the fight is quite long, and eventually healers will simply run out of mana and THEN the tank dies. In order to prolong healer mana, the tank would need as much mitigation as humanly possible. Maximum health wasnt important really, just dodging, blocking, parrying and flat armor. Healers would gear up for bigger heals and mana regen, and thus the fight just got easier and easier the more gear you had provided the tank geared for being tanky.
3 - Random Burst Damage. This method of tank damage was notably present in Black Temple era WoW, and eventually was moved away from. Here, the tank takes a constant very very heavy stream of damage, but the healers have very powerful heals and almost infinite mana. The idea being that a tank can survive maybe 2-3 seconds at max without a heal, and as long as heals are incoming they're fine, unless they take something like a double crit in a row, or two undodged attacks, or an attack and an AOE. In other words, they need to be able to survive the possibility of a big spike of damage at ANY TIME whilst healers funnelled massive heals on them constantly. The only way to gear up to survive these fights was to stack massive amounts of Health and armor - Effective Hit Points. Dodge/Block/Parry would make the bursts less common, but a tank needed the ability to survive 3 undodged attacks without a heal or there was always a risk of them suddenly dying from 100% -> 0 in 2 seconds.
4 - Predictable Burst Damage. THIS is the style that FFXIV uses in the most part. What you have is a boss that does constant damage on a tank, but in general the damage isnt particularly tough to heal through. You can generally survive it without any cooldowns, outside of your tank stance, and usually without that much health. The thing that kills tanks here is a huge tank buster move, usually on a strict timer and with an obvious cast bar. The damage incoming during this moment of Ouch is far beyond the incoming damage of the previous 3 death types, but only happens for a short time. Thus, for these encounters the tank merely needs enough mitigation to be able to survive the 2-3 second moment of tank buster - usually, popping one or two tanking cooldowns will be enough even in low vitality gear. Outside of that 2-3 second period of damage, tanking stats basically don't matter.
So those are the four ways MMOs over time have thrown damage at tanks, and you can see that for the first three tanks are encouraged heavily to be as tanky as possible at all times during the fight - the success of the fight hinges on their ability to take as little damage as possible from start to finish. In FFXIV though, that test on damage taking often only comes in very short bursts, and tanks tend to have a much larger amount of "Oh Shit" tanking cooldowns to cope with them.
When you then couple that method of tank death with the fact that: a.) A lot of FFXIV raids have very tight enrage timers. b.) Tanks can contribute almost as much DPS as a pure DPS class if played properly. The message is clear - being tanky is very much superfluous to being high damage. You can stack mitigation and health up the wazoo if you want, but it will only have a very minor impact on the success of your raid. Healers wil be able to heal you fine anyway, and all you're doing is giving them a slightly bigger cushion to allow for them to make mistakes.
That's fine... but the benefits gained from maximising your DPS output far outweigh a small cushion for making mistakes. Certainly in the early days of Alex Savage raids, fights were literally -impossible- to do without tanks meeting certain dps levels, because a raid otherwise wouldn't be able to meet the enrage timer and would die.