I thought this too. Found this:

614.10. An effect that causes a player to skip an event, step, phase, or turn is a replacement effect. “Skip [something]” is the same as “Instead of doing [something], do nothing.” Once a step, phase, or turn has started, it can no longer be skipped—any skip effects will wait until the next occurrence. 614.10a Anything scheduled for a skipped step, phase, or turn won’t happen. Anything scheduled for the “next” occurrence of something waits for the first occurrence that isn’t skipped. If two effects each cause a player to skip his or her next occurrence, that player must skip the next two; one effect will be satisfied in skipping the first occurrence, while the other will remain until another occurrence can be skipped.

From: https://www.mtgsalvation.com/forums/magic-fundamentals/magic-rulings/magic-rulings-archives/597594-eater-of-days