People dislike Hope because he comes across as a whiny kid. His grudge towards snow is also very poorly developped and as such i was unable to take it (or Hope) seriously.
Hope hated snow because he is the most salient and available target to blame for his mother's death.This is availability heuristic in action.Snow ,other than the sanctum, is most tightly related to Nora's death.Instead of blaming the sanctum, the real cuplrit and a much more difficult target to exact revenge on, hope blames snow for his mom's death.
In addition to this snow isn't exactly free of guilt either.He kept egging civilians to fight his hopeless fight against the sanctum by giving them toys and encouraging them to fight with his stupid band.
Nora makes a poor decision and joins the fight out of a strong drive to protect her son.People make fun of "moms are tough" but in fact any mother would take up a gun to protect her son in a war zone with not too many options available.
Snow indiscriminately involves civilians in his fight,never takes time to plan his actions and eventually this leads to the death of many innocents around him.Nora feels pressured to protect her son.Hope jumps on snow after witnessing the entire situation.(partially right to do so)
Hope gravtitates towards lightning because she displays strong dislike towards snow(this ties in to the snow-light-serah arc which I won't explain here)
I am fucking tired of people criticizing the hope/snow conflict(and many points about FFXIII's story) when they barely take any time to seriously analyze.
Sure the execution is a bit too melodramatic at times ,but the writing and character motivations are perfectly understandable.