Illaoi's W can force you to miss 1-2 waves each time it hits.

K so posit that you're playing a champion who CAN'T go toe to toe with Illaoi. This is most champions (that's the idea behind Juggernaut).

Say she lands a pull on you near a tentacle. You now have two options -- run or fight. If you fight, you die, because you can't go toe to toe with her, so you elect to run.

Now, at level 1 you take a full 25% of your health from this. That's forfeit. That's "whatever, she can take 25% with a single hit." If you can't sustain back 25% of your health, you're in a lot of trouble. But it gets worse.

We've already established that you can't go toe to toe, so you have to handle your "vessel" status before you go back to try farming, so you retreat to (or behind) turret to kill the tentacles and remove the vessel status. That takes you out of lane for a minimum of 30 seconds (to kill 3 tentacles). You can't go near HER tentacles, because they're also near HER, so you have to go find a spot, spawn your own, and take them down. So if we don't count the time it takes you to find a safe spot or the time it takes to return to lane, we have a flat 30 seconds minimum. In practice, of course, you lose closer to a minute.

One to two minion waves will spawn in that time. One pull from the ability... even if you have the sustain to NOT worry about the 25% health, the time it takes for you to be able to return to lane safely is enough to lose lane early.

Her W costs 35 mana. That's all it takes to deny you all that health and farm. I mean, sure, it takes more to actually engage, but pulling your spirit is really all she needs to do. It's not an expensive skill she needs to make decisions with, and if you back off, she can keep doing it over and over.