what am i doing wrong?

to piggy back off of what hybrid maenad said... if you are taking the hits OK, but don't feel comfortable, u can always use a strength potion for the initial swap. By doing this u should pull way ahead on the threat table, and then when they provoke back off of you, they are picking up where your hate generation left off.

Before a tank swap I typically pop FoF. Then I que up savage blade / voke / sprits /savage / RoH / CoS. If I can't que savage I just FoF / Spirits / solo RoH / CoS then do my typical rotation. If healers / dps are snapping hate right after your voke then it seems the other tank does not have a solid lock to begin with. Now if you took hate from the other tank and then lose it a couple mins later... well that's something on your end. Make sure you have Shield Oath up. Some of us like to squeeze the extra dps and switch to Sword Oath when not tanking the boss and sometimes people forget to switch back. Either way you should not lose hate that fast.

Most things covered already, but I didn't see a mention of communication yet. By telling people, especially the other tank, when Provoke is happening you get at least a chance of them knowing to back off for a few secs.

This can be a macro that puts something in /party chat at same time as Provoke, or something you say on voice chat, or both. There's a reason every successful endgame group uses voice chat, and this is part of it.

I also find it helpful to switch to sword oath when swapping(turning shield oath off) just a sec or two before it happens. This allows your generation to slow and allows the other tank an opportunity to build better.

There is no enmity degeneration in this game, which is kinda sad...but it's kinda important for you as a tank to know so you can better understand how it works.

Attacks increase enmity; The harder or the more you attack for, the higher enmity you gain. (Reason why some tanks will stack STR)
Criticals draw more enmity than regular attacks.
Damage over time increases enmity.
Regeneration over time increases enmity (Regen/MedicaII/Whispering Dawn)
Enmity skills increase enmity.
Provoke only sets your enmity @ 100% on the list, so if someone has DoT on it or is still using skills, then using provoke by itself is often a fruitless effort and needs to be combined with another skill to ensure you have gained full hate.

That being said, WAR can hold hate on crowds and multiple mobs much easier than PLD can. On PLD you will be mixing your only AoE attack and Flash to gain as much hate as you can on multi-mobs. Fight for flight definitely helps to make sure you keep hate starting off as well, since your attack skills are increased.

With Ex Primal fights, especially Garuda, when sisters pop, you need to stack Circle of Scorn + Flash with Shield Oath up to ensure that you have immediate enmity established on those enemies you're dedicated to pulling initially. Spirits Within and Circle of Scorn do not share the same GCD like flash, savage blade, etc, so don't be afraid to use those to try to keep enmity as well.

What is all this vague advice.

Fast > Voke > Savage > Halone
or
Heavy > Voke > Skull > Butcher

Done. Only fails if your OT is mindlessly mashing in tank stance while you're swapping, if your STR/Weapon is drastically worse than other tank (20 ilvls), or if your tank ilvls are drastically lower than the rest of the party anyways.

For quick initial aggro I use:

FoF+CoS>Flash>SW>RoH combo

Works every time.

Just to echo another comment, it could be due to your weapon. Even though it's an i100 atma, you don't get the weapon damage increase until it's fully i100 animus, so right now you are basically using a level 90 weapon with dps and healers most likely having i100/i110 weapons. Weapon damage contributes more than strength stat, which translates in higher enmity generation, so try to finish your animus asap.

Other than that it sounds like you are doing everything pretty much right (pre-loading SB/RoH, using fight or flight on CD, etc)

tank swap depends a lot on OT giving up hate. me if im MT and swap is coming even with SO ill start riot blading to allow him to take it. it makes both tanks look bad when one doesnt know swap mechanics which i dont like but on swap its mostly just timing for you. you usually have a second before swap needs to be done, load up your enmity combo even just to sb or your second war swing and provoke then immediately hit and you should have it. if youre losing it its more than likely OT using enmity combo AND thinking youre a bad tank cause hes fucking up

Check your accuracy. Maybe your RoH is missing and therefore no aggro.