Jamieson, Fausset and Brown on Matthew 12:4

4. How he entered into the house of God, and did eat the showbread, which was not lawful for him to eat, neither for them which were with him, but only for the priests?--No example could be more apposite than this. The man after God's own heart, of whom the Jews ever boasted, when suffering in God's cause and straitened for provisions, asked and obtained from the high priest what, according to the law, it was illegal for anyone save the priests to touch. Mark (Mr 2:26) says this occurred "in the days of Abiathar the high priest." But this means not during his high priesthood--for it was under that of his father Ahimelech--but simply, in his time. Ahimelech was soon succeeded by Abiathar, whose connection with David, and prominence during his reign, may account for his name, rather than his father's, being here introduced. Yet there is not a little confusion in what is said of these priests in different parts of the Old Testament. Thus he is called both the son of the father of Ahimelech (1Sa 22:20; 2Sa 8:17); and Ahimelech is called Ahiah (1Sa 14:3), and Abimelech (1Ch 18:16).