If cholesterol clogs your arteries, why are eggs healthy?

Not just cholesterol. Eggs have more than cholesterol in them. Two whole eggs (and almost unlimited egg whites) are good for you. Egg yolks have lutein, which is good for vision. Egg white are a fat free source of protein!
Protein. They are a good source of protein and vitamin d. Even people with high cholesterol can have eggs, just not frequently.