Indeed I am not interested in determining what Christians should believe. My argument is that anyone calling others pigs, dogs and swine just because they are not from his religion can't be as kind and loving as is claimed.
Jesus retort about 'in my father's kingdom, there are many mansions' was actually because he was being harassed for not having any notable worldly possessions of his own and not about him including people of all four corners of the earth in his father's mansions.
When Jesus spoke of loving thy neighbors, he is not considering any non Jews so I think you are incorrect in thinking that he is doing so. By his own words, when he called the woman a dog, he reminded his compadres even before calling her a dog that he was ignoring her because he was sent only to the lost flock of the house of Israel. They had to beg him to even look at her by telling him that her crying will befall and even then he refused saying that "it is not proper to take the children's pearls and throw it to the dogs". Nothing loving in that statement my friend.
Jesus consistently treated non-Jews with disdain.
Those are facts as recorded in the New Testament. How one choses to consider them is their right. I chose to consider them as evidence of a poisoned person.
Let me first say that your problems with Jesus calling people what they are is your problem not the problem of Christians.
The Canaanite woman knew who he was and understood his response would not thwart her request for aid. Jews did not help non jews. Jesus told her as much before his Jewish audience. She as a believer did not falter but persisted. It was to illustrate the depth of faith. And what did this Jew did for a sworn enemy of Jews? He helped her. That is the point of the lesson. Most of the stories were written some 50 years after his death and they most likely are paraphrase to illustrate his method of teaching by example and parables. Nowhere did he not help when asked.
Jesus of the bible is decisive, purposeful, and always focused on moral ways of achieving salvation. Not one line in his words ever mentioned killing anyone, or taxing them disproportionately or punishing them. He stated emphatically that the reward is not here but in another reality. Leave the unbelievers unto themselves and know they are dammed if they do not change their ways. He never suggest they be killed or forced to the faith.
Your insistence that he came for the Jews alone is not what Christians believe and what they believe is all that matters. However there are numerous examples as to why they believe as they do because they can source a reference. I do not care to quote them because I am not here to convince you but to make it clear you are spreading Muslim polemics not biblical doctrine.
As I said, these arguments are resolved for Christians. Muslims need them to establish the benevolence of Mohamed despite the reality of his life being one of war rather than convincing his opponents through the worth of his theology. Jesus never said to fight Caesar but insisted that believers follow their faith. That was was emphasized directly by his admonishing his disciples who wanted to resist his arrest and his healing the severed ear of the Roman.
The carry over of this admonition not to fight is demonstrated by the lives of the disciples themselves. Beginning with Simon to Peter to Paul to Timothy they never resisted but were martyred for their faith. While people may give their life for a lie...these people had no reason to project a lie. They believe in his lessons about peace and judgement being somewhere else.
One considers the New Testament valid no less than one considers any historical recounting valid by comparing its historical references. The people mentioned can be checked from alternative sources. Even Jesus was mentioned three times by external sources (one considered dubious because it referenced him as the son of god)
Note, the Koran is a compendium of unfinished stories of mainly Jewish life. If one is to complete any of the stories, the life of Moses's life for example, one has to go to the bible and Jewish sources. That is their historical ethos. You cannot doubt that Moses lived and had brothers, married Sephora, or that lived in Egypt and rescued his people, took them to a holy land and still have a valid Koran. If you consider that narrative valid then why do you doubt the history of lives of a people writing about their people contemporaneously in the NT? That is history; people writing about themselves. You accept it or not. And Christians do not care.