Why was San Diego called “The Plymouth Rock” of the west coast?

San Diego was the name given the bay, the presidio (fort), the mission built on Presidio Hill overlooking the bay and the town that developed along the bay. The reference you make is to San Diego, not the San Diego mission.

Plymouth Rock is a granite boulder with the date 1620 carved on it. The rock lies near the ocean in Plymouth Massachusetts. When the arly English settlers of Massachusetts landed for the first time, in December 1620, tradition has it that they stepped ashore on this rock (or more likely, historians say, near this rock).

When the Spanish first landed in California in 1769 they arrived in San Diego.

So in a very broad analogy (analogy means a similarity in some particulars between things otherwise different) both Plymouth Rock and San Diego were places where the first European settlers landed.