One explanation for vegaphobia is founded on the meat paradox: many people who eat meat do not like harming animals. Vegans remind them of this cognitive dissonance, and one way to resolve this inner conflict and reduce dissonance is to maintain prejudice against vegans.
I find it quite interesting how often meat eaters in the west will be prejudiced against people who eat dogs - as if there's any other difference than the cognitive dissonance of seeing one as a pet deserving of a dignified life and the other as a tasty steak to chow down on.