I disagree but i guess its at opinion.
As for Irelia vs Jax it all depends on what you are expecting. If you go in thinking I am going to win this lane hard becuase my jungle will gank early and we get that kill then I max W. If you want to play safer and allowing you to out trade jax I max E in lane. It doesn't help with TP ganks, but the stun duration and the huge undodgeable damage allows you to control the lane much more then Jax ever will. But this is preference.
If you really want the best commentary on irelia play you should watch
Irelia Carries U
I don't play quite as much top lane as I used to, so when im unsure of a match up ill just start the video so I can listen to his commentary while playing which gives a lot of good insight