she tanks better than pure tanks
No she doesn't, Irelia is not at all inherently tanky. It's just that she builds basically pure tank after one damaging item, but she's not gonna jump into an enemy team and not get burst down until the game drags on.
she can put out more damage than carries
*To *carries, maybe, but she's not gonna be bursting tanks down very quickly. Irelia's mostly sustained damage. Her burst largely only comes from Sheen procs with her ult.
she can get every single cs under turret indefinitely along with having crazy sustain
So don't shove her under her tower... The solution is pretty easy.
she shreds tanks and 3 shots carries
No she doesn't shred tanks unless she's bought BORK, in which case she's frail for even longer. And *most *champs late game 3-shots carries. It's just that most carries will kill them before they get those shots off.
can't push her under turret because you would basically be allowing her to free farm
So don't do it! It's easy!
can't be within 15 teemos of her or she kills you
Stay away from weak minions.