You know his next 2 moves if he uses 1 Q.
Either he wants to use W, or he'll try to hit the other 2 Q's. A good Aatrox will use them to zone because E can make Q more dangerous.
However, he's predictable in a solo situation, and should require flash to sustain a kill. Aatrox is actually pathetically weak if you just get up in his face. He can be 3 kills up and if you're a decent melee champion -- you'll still beat him or force him back if he can't land the third Q on you with passive. All he has is W to peel you off, and if that's gone, as almost any bruiser you can be aggressive on him, ignoring his autos. If you make the first moves as well, his first 2 Q's are worthless and he needs W. Bait it out or wait for it to be used, kill him -- alternatively simply outplaying it knowing that it's coming and has a cast time.
Early on, the cooldowns are quite long -- he can just space out the Q's to make it seem shorter. You're able to just be aggressive when he wants to zone or trade with you because the second Q will be utterly useless, and you then know there's only one ability left to him -- which makes it easier to play around and even then not too much damage in comparison to what you will be dealing out continuously because he can't stop you after that, even if you have half hp -- you're going to make him pay for that trade with more. If that misses, you zone him now. The lane is about not relinquishing it to Aatrox containing zoning abilities because they're very punishable by confident plays and quite awful actually at extended dueling. It's a kit that punishes passive players or ones that are too afraid of his abilities rather than those who are actively engaging in lane dominance at good intervals. Engaging when the passive is down is the main prerequisite, which you can tell by how he holds his sword and when he strikes.
Late game, he still dies if you just jump him and his ult is down. His close range abilities are garbage. If he uses W on you to get you off, moving to the side cancels the chain and makes his third Q very difficult to land anyway and even allows you to outplay his third Q with his own W. Aatrox's kit counters himself in solo queue, it's very readable -- you just have to choose your action or reaction intelligently enough to punish. It's a little ironic how much counterplay is in his own abilities.
Coordinated play though, he's busted. Can't go silly aggressive without knowing about junglers or roaming laners or another quick TP behind you -- and that lets Aatrox control the lane because he has zoning abilities built for control over actual dueling, something which normal engage aggression would counter but is discouraged due to a high variety of punishes by the enemy team that are possible. Then he just has his ultimate as a safety net to frontline for free or get out of a high damage rotation or bad spot. Great champion in a competitive environment. Relatively garbage in solo queue if your team isn't recognizing you have an Aatrox -- which the latter opposite tends to happen at higher elos and open up his abusive laning on an opponent that can't engage when they sorely want to. You'll notice even in Worlds how if an Aatrox is caught out and not 3 kills ahead, even the enemy top with a kill below and 30 cs down, or even the jungler with half an item less can just run at him while the team 4v4's mid, with murder in their eyes and the Aatrox has to flee because aggressive dueling simply outpaces his control in most cases.
Know your own champion, know the enemy champion, and abuse accordingly. Some have less windows than others. Aatrox unfortunately, has Ryze syndrome. Game has a lot of facets and a plethora of abilities, champion matchups, and mechanics which are exhausting to keep track of constantly at every second of the game. It's natural that you will learn as you pay attention and grow.
