Everyone thinks Darius counters anyone who's melee, except one...

I have to admit it. I know what Darius can do in order to rekt a ton of enemy melees, be it a Riven or not. But when it comes to a highly experienced Irelia, oh boy o boy, I never had someone who can get my day frustrating as fk.
For instance, she can do a surprise gimmick on me by Q'ing a 1HP minion near me & starts engaging. Only when she notices that I plan to use my Q, she would use a direct Q on me, closing the gap of my axe. Even if I were to be on the Offence using plaining my AA & W, she outsustains & outdamages me due to her True Damage & HP gain per AA kits, especially when she hits W & R (even her ult heals her...).
I mean these are just what I think about the Darius vs Irelia matchup. So tell me guys, do you think it's:
- Irelia being an excellent counter to Darius?
- Irelia's kit is just broken & a tad overloaded?
- me being a noob on Darius?
What do you think?