The show bread was "for Aaron and his sons" (Leviticus 24:9). Why does Jesus bring up David eating it?

The law says of the bread set before the LORD, "It shall be for Aaron and his sons. They shall eat it in a holy place" (Leviticus 24:9). At Nob the priest gave it to David after asking one thing, "if only the young men have kept themselves from women" (21:4), and David answered that they had (21:5). 1 Samuel 21 doesn't say whether the priest did right. Jesus calls the bread what the law made it: David ate the show bread, "which is not lawful to eat except for the priests alone" (Luke 6:4). He brings it up when his disciples had plucked heads of grain on a Sabbath (Luke 6:1) and some of the Pharisees asked, "Why do you do that which is not lawful to do on the Sabbath day?" (Luke 6:2). Each Gospel tells what he said with it. In Luke: "The Son of Man is lord of the Sabbath" (Luke 6:5). In Mark: "The Sabbath was made for man, not man for the Sabbath" (Mark 2:27), and "Therefore the Son of Man is lord even of the Sabbath" (Mark 2:28). In Matthew he adds that "the priests in the temple profane the Sabbath and are guiltless" (Matthew 12:5), and says, "But I tell you that one greater than the temple is here" (Matthew 12:6), "But if you had known what this means, ‘I desire mercy, and not sacrifice,’ you wouldn’t have condemned the guiltless" (Matthew 12:7), and "For the Son of Man is Lord of the Sabbath" (Matthew 12:8). He gives these together, and he doesn't say David sinned.