Team fights are hard on him because his early game numbers were tweaked to make him take longer to scale upwards. This was evident in his further fall throughout Season 4. With the amount of dashes and peel that teams can employ, Jax's one shot at his E Q (E has a huge cooldown) makes him very vulnerable. The moment you pop E, you've put a target on your back and one ability that can knock you out of position will hurt. Also, people have to realize that his E's strength is to block auto attacks. The longer you keep it up, the more you'll absorb. The problem is, in team fights, you're not going to get by only AA's. You're going to be dealing with the back line peel of an AP champ most likely also. If he doesn't land his E, he's basically done unless he's already been fed (And let's be real, just about every champ has this going for them if they're fed). His ult MR/Armor is so overrated and it still doesn't allow him to be the main tank/initiator. He's more of a weak offtank that has really only one form of CC that requires him to leap and usually flash in order to catch up with all the mobility these days.
Jax has always been oppressive when fed; what champ isn't? The number of times I've come out in lane throughout Season 4 and been fed and been able to dominate people is countless. Usually I'm not able to 1v3 or anything crazy like that because it wasn't in normals or preseason (which everyone takes waaay too seriously), it was in ranked where people my skill level knew what to do to beat me. Hell, I would say Irelia is so much more worse than Jax. If Jax gets shut down in lane, he's not coming back. If Irelia gets shut down in lane, she picks up a Triforce and all of a sudden it's as if she never lost lane. You want to talk oppressive, where's the complaints for Irelia at? That's a discussion for another time though lol
The most frustrating to lane against, as Jax, has to be Renekton. He has built in armor pen, built in sustain, a lock on stun, two dashes, and one hell of an ult. He dashes in, stuns you, does his damage, and dashes out. When I usually play against a good Renekton, it's game over. I'm not beating him without a gank. It's been awhile since I've seen an actual Renekton main that knows what they're doing but when I go against one I can't really do anything. He zones and bullies well, as he was intended to do. And Jax isn't someone that really comes back from being behind. The Triforce is a 100% necessary item on him and even then, it doesn't work as well as it does on Irelia.
Anyways, I kinda went in depth with some stuff but meh, just my two cents.