From wikipedia:
The movement's popularity [Hamas] stems from its provision of welfare and social services to the Palestinian poor, comprising over 80% of its budget (such as its involvement in building schools and hospitals for them) and from its homicidal attacks against Israelis
I don't think this is living to hate. While hamas is recognized with suicide bombings due to media's coverage of this aspect, inside palestine the social and welfare activities seem to be the source of the popularity - considering, the fatah party is pretty much corrupt (Arafat and others).

Of course there is a lot of hate going on there, from both sides and they can fight a few more decades as far as I care. But hopefully they will realize they cannot solve this issue with violence and destroying Israel is a really stupid goal.