Matthew 12:5

“Or have you not read in the law, that on the sabbath day the priests in the temple profane the sabbath, and are guiltless?”

But he also has a second argument (which is not mentioned in Mark and Luke), and that is that the priests in performing their functions of worship are constantly technically breaking the Sabbath by carrying things, slaying sacrifices, and so on. And yet they are looked on as guiltless because the authority of the Temple overrides the Sabbath Law. His point therefore is partly that everything is not just a matter of ‘black and white'. There are various shades of grey. And so each case needs to be examined on its merits.

We can understand why Mark and Luke omit this section. To most of the people to whom they were writing the Temple ordinances were unimportant and not significant. To Jews and Jewish Christians, however, they would be of great importance, especially before the Temple was destroyed.