It wasn't fear, it was practicality. When your tribe expands beyond the supporting capacity of your territory, the only way to avoid starvation is to invade your neighbor's territory.
As far as how Cro-mags killed off Neanderthals, a moderate advantage in speed or throwing ability translates into a BIG military advantage. If you can creep up to your enemies, throw spears at them from longer range than they can throw back, and then run away faster than they can follow, it would not take long to wipe them out.
And you either take that territory or solve your overpopulation problem trying.
That THEY were shocked is saying something ... coming from Europeans THEMSELVES survivors of decades of internecine, abjectly bloodthirsty religious wars and wars of succession.