How is fleas harmful?

Fleas suck bloody from animals, similar to mosquitoes. Upon injection they inject an anti coagulant into the blood, making it easier to suck. This anti coagulant is what causes the itching and the swelling involved with a flea 'bite'. This in itself is not really harmful, more irritating. However fleas can transmit very harmful blood borne diseases like Bubonic Plague or malaria.

Instead of the bite being harmful, it is what the bite can transmit that we need to worry about.