Cowboy Bebop at His Computer: A common and repeated criticism of Cyclops' behaviour post-AVX is that he seems to always hide behind the excuse that the Phoenix made him kill Xavier, or blames everything on the Avengers, instead of accepting blame. In the actual comics though, he's actually shown to be feeling a great amount of guilt over what happened, even becoming a Death Seeker, and his current motivation is that he wants to make up for what he did by saving the mutants now in danger, but at the same time, he resents the fact he's held accountable to everything that happened. It seems people ignore the former point in favour of criticizing him for the latter, which becomes pretty unfair given that the Avengers and Wolverine's side of the X-Men (save for Captain America, slightly) have all refused to accept any blame in the mess.
A lot of people not aware of the comics only regard Cyclops' power as your token ranged attacker, i.e. the eye beams are similar to a laser gun or bazooka. His brilliant tactics and melee combat skills are often untold and undermined. The film trilogy didn't help, either.
His leaving his wife is summarised as him being a deadbeat who immediately abandoned his family when Jean came Back from the Dead. In reality, he didn't even abandon her, he wanted to see if Jean was really alive, she got mad and told him not to come back, and he ended up getting busy with X-Factor, a team he wasn't even planning on co-founding and didn't want to be of at first; then when he did go back to her, she'd already left thanks to a supervillain attack. He's by no means unblamable, but he's not the deadbeat dad people often claim him to be.
Having an affair with Emma Frost while married to Jean Grey, the. Kissing Emma in front if Jean's grave. Usually summed Up as Cyke being a horny jackrabbit. However, Jean herself contemplated having an affair with Logan while Scott was in the middle of an emotional breakdown, which Emma took advantage of. Emma was Scott's therapist at the time, and she told him that the best way to deal with his problems was to have psychic sex with her. So basically, he was raped and is hated for it. And Jean actually used her abilities to force Cyclops into loving Emma via Mind Rape. So he was actually raped by two women, and those two are either treated like saints who could do no wrong and had a crappy husband (Jean) or are rewarded for their unethical behaviour (Emma).
Going nuts with the Phoenix Force and killing Xavier. Cyke actually tried to make the world a better place, albeit in the worst possible way (he basically told the entire human race that they had no choice but to live in the paradise he was building, regardless of whether or not they actually wanted to live in his idea of paradise, effectively turning the world into a police state) and it was his teammates who were losing their shit, at least quicker than he was. Furthermore, he never attacked the Avengers even though they repeatedly antagonised him. The only reason he killed Xavier is because Xavier outright said that he was going to Mind Rape Scott. This is something he has done previously, to the point where he actually did Mind Rape Scott of the knowledge of one of his brother's existence. Scott was acting in self-defense, even though by this point he was pretty much losing his shit. About half the fanbase seem to blame Wolverine, Captain America, and Iron Man for this one, but Cyke is still, in-universe and out, considered the one responsible, and is so far the only one to get any blame for it.