Any list that only mentions her strengths is useless. Also, I see you just got wrecked in a match by a very fed Irelia. Any fed champ is "OP".
Yes, she has a strong laning phase, and is a duelist so don't expect to 1v1 her with anything other than a duelist. She doesn't have a "hard" counter. She fits in too well to too many team comps (i.e. when is it ever a bad idea to pick her?). She's also strong mid game, especially if ahead. She falls off later but still serves a role well (changing from more of an assassin/fighter to pure fighter/off-tank.
She's also very vulnerable to CC early game. The tenacity helps her, but even soft CC like slows makes it fairly easy to kite her. Most people make the mistake of throwing their CC out immediately, then she just stuns or slows you and sticks to you. Also, if you position appropriately, she only has an in - once she goes in, she has to all-in or likely lose the trade...easily exposing her to ganks. Unless fed, since she's a duelist, she can't handle 2 champs coming at her (unlike Darius or something who is strong early and has AOE and a reset to deal with multiple targets).
Anyway, the biggest issue is that she's a duelist so the way you win is by not dueling her without a significant advantage. Don't play her game and she won't ruin yours.