Actually, if you get Javik and Liara to console after Thessia it's pretty clear Javik has come to care about her. He consoles her after the Sanctuary mission - Tali even teases him about liking her - and given the option he chooses to write a book with her even when he knows that he could go to Kahje and live like a king. Yeah Javik insults everybody and is a jerk, but so is like half of your squadmates in ME2. P: He's a complex character and you can't dismiss him as just that.
And yes, he does insult Liara. They don't initially get along and argue and bicker and dislike each other a lot but they eventually grow and respect one another.
You know who else was like that?
Joker and EDI. And to a degree, Garrus and Tali. And look what happened with them.
To be honest, I think if you where the only one thats left of your race, it would take time to trust somebody-especially the races you studied ~50.000 years ago when they where primitive. Like Zaeed says to Samara-everybody has a soft side. It just needs some time and beautiful asari.
There's that too, especially when Javik had to deal with indoctrination so up close and personally like he did. After something so horribly traumatic like that, it would be difficult for him to really get attached even if his culture wasn't so xenophobic and imperialist as it was.