The flippant remarks aside, Christ says doing good is lawful, and I believe him.
The very core of God's Salvation is centered on "Belief". Not just belief in a Word of the Christ here or a Word there, but belief in all of the Words the Christ Spoke as recorded in the Moses and the Prophets, and the New Testament where the Word of God who spoke to Moses, "Became flesh". I wasn't being "flippant" at all in my reference to believing God.
Christ's example in Mat 12 is regarding sheep trapped in pits (not actually oxen).
Let's look at what is actually written in this Story you are using to justify working for others on God's Holy Sabbath.
Matt. 12:
1 At that time Jesus went on the sabbath day through the corn; and his disciples were an hungred, and began to pluck the ears of corn, and to eat. 2 But when the Pharisees saw it, they said unto him, Behold, thy disciples do that which is not lawful to do upon the sabbath day.
It was not against the Sabbath of the Christ, the Holy One of Israel, as defined in the Law and Prophets, to take a walk in fellowship with HIM, and pick a blackberry or ear of corn along the way to munch on. A Core, and undeniable Truth of the Holy Scriptures was that the Pharisees
didn't believe Moses, nor did they believe in the Laws, Statutes or Judgments that the Spirit of Christ gave to Moses. They had created their own religion, with their own sabbaths, their own judgments and their own righteousness. This undeniable truth is not taught by this world's religious system. Nevertheless, according to Scriptures it is true just the same.
The reference of the sheep in a pit, was used to expose their hypocrisy, expose their teaching. What the Disciples did was not against the "Law of Moses" or as it is said "Unlawful". It is good to walk in fellowship with Christ on the Sabbath, and there isn't any law against eating a raspberry along the way. Just as there isn't any Law against pulling a sheep out of a Pit is has fallen in, or sharing the Word of God with a neighbor on the Sabbath days..
But Jesus didn't clean Peters boat, or take the Apostles fishing, all of which you might judge as "Good", and therefore Lawful.
We look at this story in a different Light. You want to work on God's Sabbath, and exact your pleasure as well, no doubt. It's a perfectly acceptable tradition of this worlds religious system, to treat God's Sabbath Day no different that any other day.
So you look for Scriptures that you can use to Justify this popular tradition. I don't, because I believe in the Christ when HE says,
"Remember the sabbath day, to keep it holy. Six days shalt thou labour, and do all thy work: But the seventh day is the sabbath "of the LORD thy God": (This is the Jesus "of the Bible", Yes?) in it thou shalt not do any work, thou, nor thy son, nor thy daughter, thy manservant, nor thy maidservant, nor thy cattle, nor thy stranger that is within thy gates:
It's simple, you don't believe the 7th Day is Holy. If you did, you would mow your neighbors Lawn on Thursday. And invite him over to your house on the Christ's Sabbath to fellowship with the Christ, and feed him cake you cooked on Friday.
There is no reason to address any more of your post. It's all for the purpose of justifying popular traditions. I know because I lived by the same traditions "
Wherein in time past I walked according to the course of this world, according to the prince of the power of the air, the spirit that now worketh in the children of disobedience".
Perhaps the Sabbath doesn't matter, but the reason for my post is to show that in Matt. 12, Jesus wasn't promoting the creation of a 501c3 that mows the yards of random people, only on Saturdays.