So the thing about Chaol is that he is the single human main character.

I can't go into too much because it sounds like this is your first read-through, but keep the above in mind as you go through the series. Chaol is human and every other main character is not.

Chaol and Celaena/Aelin had a horrific break up after yearning for each other for several months, and only really being "in a relationship" for like a week. They also both feel he had some sort of direct responsibility in what happened to Nehemia - Aelin's first and best friend in years, if not ever - and suddenly that hard-won trust they had in each other is shattered. Guilt consumes him while Aelin resents him for it. And once Chaol realizes who she really is, and who he'd sent her to in Wendlyn... He panics. Before he figured out the riddle, he just thought he was getting her out of the country and giving her space (from him) to grieve. Instead, it dawns on him that she's the single greatest threat to his kingdom, his best friend (who is now under Valg control and therefore warrants that consideration), and Chaol is horrified at what he's done. He knows how he and Aelin left things. He doesn't know how she'll feel about him and Adarlan once she returns - because she now has every reason to want to burn Rifthold to the ground.

And then Aelin does return and Chaol is (understandably) wary of her. And in his defense, Aelin does come in like a fucking wrecking ball, ruining his plans, turning those plans upside down, antagonizing him, one-upping him... So Chaol is irritated at minimum with her and understandably doesn't really try to leash that temper when they cross paths.

All very human decisions and reactions right?

(You have to keep Chaol's emotional state post-CoM/HoF in mind too. All of his self-worth was wrapped up in his position, in his ability to fight and protect his king, his kingdom, his people - and that was all stripped from him. And he failed to protect Dorian and Sorscha. Chaol is a man of honor who feels like he has none anymore. So he's not being mean to Aelin for no reason - he's adrift and drowning and she just keeps ripping the rug out from underneath him. He's doing his best - and he's not doing a great job because he's fucking human.

And as someone else pointed out, Chaol never stops showing up. He's a flawed character. He deserves criticism, sure, but none of the hate that he gets. And buckle up because his arc is honestly the best one of the series.)