The issue is that it was not a violation to graze on shabbat, only harvesting is a violation. Breaking in general is an add on in the "oral law".So... just in regards to food:
In Mathew 21:1-8, Jesus's disciples were being jammed up by the Pharisees for doing what was unlawful on the Sabbath, namely picking grain to eat.
Jesus had a 2 point rebuttal (which is really just one point), but the first of them is in verses 3-4. There are many avenues He could have chosen to pursue in His disciple's defense, but He chose to make His primary argument a strange tale of David eating the shewbread, which was not lawful that he or his men should eat.
As to why Yeshua chose to answer in the manner He did can be for many reasons; we can all speculate as you have here but our speculation can not take us out of bounds so to speak.
My first thought was that He knew their minds and perhaps they expected him to respond "that's just your traditions" but He's done that elsewhere so instead He uses a principal which they would be familiar with against them ... pikuach nefesh, "life risk" When there is a time of war or food scarcity and a risk of serious illness or risk, almost any command can be broken because to preserve life is the purpose of the Torah and in His case to make it more abundant even. He sides with Rabbi Hillel in most of these cases so it seems to me He ingeniusly uses in house debates among the Pharisees with whomever He's speaking.
In this case, it's over the issue of pikuach nefesh. ... brilliant!
To jump to a conclusion that He's beginning a slippery slope to allow all kinds of violations is not warranted and would make Him into a rasha (wicked person) by Torah standards, especially regarding the sabbath with it's looming death penalty for violation.
He'd be an unfit sacrifice to say the least if He "taught others to break the least of the commandments"
no...David was at war and you can eat even pork to have your strength so you don't die in battle...To which I say that the eating of food that is prohibited by the Law, is yet not a transgression of the Law. Or if it is: it is a transgression that is specifically allowed by Jesus Himself, and the man who does so under these circumstances is held blameless. The circumstances are: You are one of the King's men (a disciple) and you are hungry...
simple pikuach nefesh case, Rabbi Hillel, writer of the L-rd's prayer wins again (as decided by Yeshua)
Taken together with God's command to Peter (Arise, Kill and Eat), I think it to be reasonable for a man (yea, even a Jew!) to eat things that the Law would say no to all day long, but still not be held in contempt of the Law, as God understands it and intends it to be understood.
Nope, Peter remained righteous and never killed because He knew from his vast training with the Messiah that G-d would never intend for him to do such a thing (remember the whole straining to keep unclean gnats out of food 'you'd do well to leave also the little things not undone'... good thing he kept his whitts about him and passed the test! He never ate and never was rebuked for it. I love how consistent scripture is.
I love how G-d isn't sneaky with His expectations of us and to a 1st century Jew of faith like Keyfa, He passed His test this time.
A side thought I posted in a different, now locked, thread. What does food in a vision taste like?
How do you kill it? Do you use air arrows and then clean it with an spirit knife (sword of the spirit perhaps?)
Do you cook it up on an air flame? I bet vision food tastes like spirit chicken.
Yummy!
Vision food .... it's what's for dinner!