How do I get rid of eggs?

Solution 1:

There doesn't seem to be a way to remove eggs as of this moment. Seems like the only way is to hatch them.

Source: Multiple mentions of it on Reddit.

Solution 2:

It is indeed impossible to get rid of your eggs other than hatching them. Although your theority about the distance needed for the eggs to hatch and the likelyhood of a rare pokemon has been confirmed.

Solution 3:

As of this update, there is no clear way to get rid of eggs.

The best and only way to get rid of eggs is to hatch them, you have you walk to hatch them. You have to hatch them to get rid of them.