The reason why driders were hated was because they were an imperfect form, caught half way between a drow and a spider. The drow recognizes the driders as failures in one of loths tests, therefore they are weak and should be killed. The driders feel shame and hatred towards the drow because of their transformation. The fixation with spiders is also part of why drow are insane, because they wish to emulate the spider, which is the sign of their god; which they can't do without magic. The drider is like the half completed failure to this emulation, so the drow hate them for showing that they can't accomplish the emulation of their god.