They don't. The Cybermen's emotions are suppressed, so they don't hate anything. However, Daleks do hate the Cybermen (along with every non-Dalek lifeform) & therefore seek to exterminate the Cybermen (again, along with every non-Dalek lifeform). In response, the Cybermen fight back.
The two species' attitudes to each other were shown particularly clearly in "Doomsday": The Cybermen proposed an alliance with the Daleks. The Daleks rejected that proposition & started exterminating Cybermen. When told that they'd declared war on the Cybermen, the Dalek leader (Dalek Sec) replied, "This is not war. This is pest control."