Abiather or Ahimelec? Did Jesus quote the wrong guy?

Did Jesus make a mistake in Mark 2:26 by saying Abiather the high priest when actually Ahimelec, Abiather's father was the high priest when David ate the shew bread?

The words of Jesus do not mean, "Abiather was the high priest during that time", they mean "During the time of Abiather, the high priest", even though Abiather has not yet become the high priest.  In retrospect we generally say ,"During the time of King Asoka ",and narrate a part of his life when he was still a prince or "In the life of the Buddha", when the Buddha had not yet attained the buddhahood and the title "Buddha", but still during his lifetime. So Jesus was narrating it retrospectively and so his statement is consistent with the truth.

So Jesus was right in saying this,"Epi abiather archiereos",  which means "in the time of abiather, the high priest" .  

According to Norman Geisler and Thomas Howe, here is one way of dealing with this problem:

First Samuel is correct in stating that the high priest was Ahimelech. On the other hand neither was Jesus wrong. When we take a closer look at Christ’s words we notice that He used the phrase “in the days of Abiathar” (v. 26) which does not necessarily imply that Abiathar was high priest at the time David ate the bread. After David met Ahimelech and ate the bread, King Saul had Ahimelech killed (1 Sam. 22:17–19). Abiathar escaped and went to David (v. 20) and later took the place of the high priest. So even though Abiathar was made high priest after David ate the bread, it is still correct to speak in this manner. After all, Abiathar was alive when David did this, and soon following he became the high priest after his father’s death. Thus, it was during the time of Abiathar, but not during his tenure in office.