She can trade. Its just not stellar without certain things being in her favor.
She can't ignore minion advantage unless her ult is up, which makes it more than a simple trade. Her E has nothing to do with it. It should just be considered a stun, plain and simple. Treat it the same as you would if you were fighting Renekton, except Renekton's trading is even more bullshit.
She doesn't win trades even if she loses them. She wins trades if you're stupid about your trading. If you do that more than once, you're even more stupid.
You have two choices: Actually learn the match-up+trading stance, or keep complaining and losing to her.
The majority of champions have a safer way to farm than her. The majority of champions can freeze/break freezes better than her. The majority of champions teamfight better than her. Irelia has her mid-game assassination period. That's pretty much the majority of why she's strong. Stick around your squishies and you'll see why she isn't picked competitively right now.
If you can't push her out of lane, just don't feed her. Farm and build properly so she can't all-in you at any time for a free kill (which should be happening as any top laner). If you make it to teamfights without feeding her, you win if you're playing properly.