Even before the Mosaic covenant that came to Israel at Sinai, what had been Israel’s responsibility? According to the Abrahamic covenant, it was to be a light to all peoples that they might reveal the glory of their covenant God, which would be done through the demonstration of divine blessings that would come from their living as their God’s covenant people---exemplifying divine blessing. After the exodus, they would show forth this covenant by keeping their God’s Sabbaths, reverencing His sanctuary, and by not worshiping idols. Through this, their God would show Himself, through Israel, as the Lord of all creation.
This could engender hate in two ways, and this entails a shift from history to philosophy, attempting to make an appropriate application of these words. The first way that could engender hate would be based on the fact that humanity, beginning with Adam, has been rebellious, not wanting to submit to its Creator God, and certainly not wanting to have their self-erected gods dismissed. Therefore hate is directed towards those that reveal a God that rules over all and demands (deserves?) unswerving allegiance.
The second potential reason for being hated is their presentation of themselves as the Creator God’s chosen people, through covenant, and then not living in a way that reflected that idea and which did not honor the blessing---by engaging in idolatry or by turning inward so as to keep their God’s blessing only for themselves and excluding those that they felt were unworthy of the covenant. The second reason is quite compelling. Can this be applied to the words that Jesus directed towards His disciples, which His disciples would in turn purposefully direct towards His church? Perhaps.
What is a fundamental obligation of the person that claims to be in Christ? Is it to judge people, to regulate their lives, and tell them how to live? No. A thousand times no! Unfortunately, this is what usually generates hatred. However, is hatred that stems from doing that which Jesus has not obligated His followers to do, really the hatred of which Jesus speaks? Probably not. Beyond that, are people going to hate believers, or would they have so fiercely hated and persecuted the early followers of Jesus if all they spoke about was escaping off to a heavenly island of peace and bliss following death? Again, probably not.
So why would there be hate? Well, as it was for Israel, so it would be for the new covenant people of the Christ’s church, as such people went and go about the business of their primary obligation to proclaim that Jesus is the Lord of all, and that all are subject to Him and to His rule, without exception. Quite naturally, this can produce hatred, as it attacks the root of what seems to be mankind’s primary problem, which is the misuse of the divine image, as that divine image bearing is turned into self-worship and a thirst for power rather than being exercised in the reflection of the Creator God’s glory into His world.