Website owners don't like CPC because the advertisers try to push branded ads that don't ask for a click (essentially free advertising). It was only with the ad

Website owners don't like CPC because the advertisers try to push branded ads that don't ask for a click (essentially free advertising). It was only with the advent of Adsense that CPC became acceptable due to super efficient targeting, and even then it's often used as a last resort to fill unsold space. Advertisers want CPC/CPA because it allows them to sit back and get the publishers to do the work, whereas CPM allows the publisher to concentrate on their website's content rather than targeting someone else's ads.