The protoss have a history of racism and the whole "manifest destiny" shtick going for them even before the Aeon of Strife (when the xel'naga last had contact). It is reasonable for the Overmind to assume the protoss would exterminate the zerg even if the zerg did not initiate hostilities (fat chance of that happening, since their shtick is to consume the strongest species they find in never-ending pursuit of fabled perfection... surprise, surprise, the protoss almost certainly fit the bill).
The
Liberty's Crusade novel explains that the zerg describe the protoss as genetic xenophobes who exterminate any life that grows beyond their control or does not meet their standards of perfection, while the zerg by contrast are genetic survivors that hunt other species as food and raw materials. This is not stated in the manual, sure, but unlike Metzen it doesn't pointlessly contradict the manual.
This traps the zerg in a seeming catch-22: either they can wait for the protoss to kill them for being ugly, or they can bring the fight to the protoss and get a nice pair of genes out of the ordeal assuming they can find a determinant that may not exist. No surprise they chose the latter, a la "do not go gently into that good night."