Why is Jax not used against Irelia?

Irelia's laning phase is much better than Jax's around lvls 4-10 she would win most of the time in all-ins. At lvl 11 Jax's passive damage becomes to much for her and he will always win duels (unless she is ridiculously fed). Jax will always out scale Irelia if he builds correctly. Get a Trinity force and BoTRK then tank and Irelia will never be able to beat you.

Yes.

Essentially, Irelia > Jax with the nerfs.

Irelia favors short engages for 1-5 seconds, where Jax favors longer, drawn out engages giving him time to stack his passive

Jax can beat Irelia. But Irelia can also beat Jax. Kit for Kit though, Jax wins. The Irelia player has to out maneuver the Jax. But if they went straight AA war, Jax would win regardless. Irelia has to gain a substantial lead on Jax though. If the are even or close to even, Jax wins post 11.