score:12
The very next chapter indicates that Ahimelek had a son named Abiathar.
Priestly duties were typically within a given family at one time (eg Aaron and his sons). The title of "high priest", while alone at any given time, does not preclude there being other priests (otherwise Aaron and his sons would have all been "high priests" - whereas "high priest" indicates a specific level of duty to the Lord over and above that of a 'normal' priest).
Upvote:3
This is a good quesiton. However, the point here is that it is important to notice that Mark says he went to the house of God "in the days of Abiathar the high priest." Ahimelek was the priest who was present at the House of God.
As Warren has answered, there are multiple priests at the time. When Saul learned that Ahimelech helped David, he commanded to kill Ahimelech and his family (1 Sam. 22:18-19), leaving alive only one of his sons, Abiathar the priest who was lucky enough to escape.
Upvote:5
If you're describing something that for example, the American president did before he was president you would still refer to him as President Obama would you not?
Mark does not say that he was literally the high priest at the time. It was however, in his days - when he was alive.