Jesus' logical fallacy when failing to wash his hands.

Jesus historically seeks occasions to teach, and his philosophical anchor is that he understands what "God" cares about, better than others, such as Pharisees. He has biblically been known to refer to the mote in one's eye (it makes us blink) in comparison the "beam" (a large log) in the opponents' eyes. The fallacy is the idea is that perfection is the enemy of the good.

On a purely logical basis, there's no final answer imo, and we humans only approach the perfection of a circle (eg) with an infinite set of polygon lines, or use the taut line of a radius to find the reality by the analog, not the digital approximation.

I guess it is debatable whether or not this is it he context of an argument. Jesus also wasn't asked a direct question or prompted to respond to the criticism. This is akin to

"You're late!"
"Yeah? Well you're ugly."

There is no denial of the accusation; it is more of a redirection of focus. In the Jesus example, according to my interpretation of the story, Jesus is pointing out what he believes is a larger issue. "Whataboutism?" I think a good case can be made that this would fit under that label.