Catlyn was likeable because other than the whole Jon killer fantasies, she was an all right person. A terrible statesman, but Tywin was a good statesman and that didn't make him likeable or a good man.
One can argue how much at fault Catlyn was, for she didn't go full retard over nothing. There was the letter by her sister (who sent it on Littlefinger's orders) telling her the Lannisters killed Jon Arryn, her husband's adoptive father getting killed (on Littlefinger's orders) and then her husband's best friend asking him to replace the man who just got killed by Lannisters (but didn't actually, but she didn't know) in the town full of Lannisters, the assassination attempt on cripple Bran (legitimately not Littlefinger's fault) which she found evidence that Tyrion was behind (the evidence fabricated by Littlefinger) and her kidnapping Tyrion is what instigates Tywin to lead raids upon the riverlands - making war inevitable. And the Littlefinger gives Edd a little nudge in the right direction to discovering the truth that Jon Arryn had discovered, namely the truth behind the Lannister children's lineage.
And then Ned Stark's one chance to fix everything and install the lawful heir Stannis Baratheon to the throne after Robert's death is foiled by Littlefinger. Which results in the dying of Sean Bean. Guaranteeing the Clash of Kings as Renly, Stannis, Balon, Joffrey and Robb (and technically Mance) all get antsy in Westeros. It is also notable that, while Varys handled all of the Iron Throne's assassination attempts on Danaerys, all of them failed. The moment Varys and Littlefinger both agreed that Danaerys had to be assassinated... Surprise surprise, the assassination is only foiled by a conscientious and guilty Jorah Mormont. Also, there's no surprise that Littlefinger when talking to Ned Stark proposed using Joffrey as a puppet King, and should he not become a King they like, expose his secret and replace him with Renly, not Stannis (as they could then use Renly's secret to control him) - and then Renly legitimately weights his claim after this. ALSO Littlefinger was a major source of Baratheon bastards via his brothels. No surprises there either, which is why I also believe he may have found Gendry - he has an affinity and an interest in knowing their whereabouts. He then negotiates the prisoner exchange which makes Catlyn go full retard and screw over the king in the norf and guarantees that Robb Stark (who had otherwise been completely victorious in the war) was fucked, as the Karstarks returned home and the Boltons grew agitated. Littlefinger is then the one to negotiate the Tyrell-Lannister alliance, thereby stopping Stannis from taking King's Landing and ending the war. Littlefinger ruined the chances of two good Kings to end the war. He's a dick like that. He then engages in next level political dickings by marrying Lysa Arryn, then begins fucking around with Tyrell and Lannister attempts at marrying his new waifu, Sansa. Oh, and somewhere in there Littlefinger sends one of his rentboys to being literal political dickings with Loras Tyrell to get the edge in the Tyrell-Baelish politidickings. Then he assassinates Joffrey, plunging the court into yet more chaos with Tyrion being a notable casualty for the cause of the iron throne. What a dick. He then kills Lysa Arryn after telling her that he only ever loved her sister. What a dick. The only good thing he did really was help Sansa escape (which is undone in the show as he quickly puts her in danger by putting her in the Ramsay sexy flying flaying naked ninja court of 20GOODMEN) and nurture Robin Arryn, who everyone dismissed as nothing more than a sickly boy - of course with Littlefinger reminding them that sickly boys can become powerful men... With the reminder that Littlefinger was once a sickly boy being picked on by Stark ubermenschen, and by the end he had orchestrated the deaths of most of the Starks. Not gonna call him a dick for that one, there's too many factors at work to make it black and white.
He then screws over Brienne and Pod, but really this bit is more Brienne's fault for being lawful stupid and a failure of a bodyguard. Nice person, but seriously everyone she swore to protect is dead. She should have told Catlyn to shove off with her crap about freeing Lannisters... Moving on. Littlefinger then continues to screw over the seven kingdoms by betraying the Lannisters in favour of the Boltons (by marrying Sansa to the Boltons), then screwing over the Boltons by revealing this to Cersei and getting Lannister support for an invasion of the North, then screwing over Cersei in favour of the Tyrells by revealing Lancel Lannister's secret sexy time to the faith militiant.
What a dick.
I could be misremembering but I swear Cersei was like "DO SOMETHING, HE SAW US BANG!"
Considering their incest was what led to her ending up in religious prison....she had an interest in making sure no one found out about it too.
Cersei was of the opinion that she could just intimidate Bran, and for that matter just intimidate Jon, and also intimidate Ned. She used to not think killing people first and deescalating later was the better option. Then she killed the King. After that she started killing everyone.