I agree with approaching people with the loving truth of God; however the dog analogy isn't far off, because some people literally think they are dogs. It is part of the dissonance-driven culture. People must not let their dissonance and their feelings define them, but instead surrender those feelings to the Spirit of Truth and letting him dismantle them by revealing their source and removing them.
The Gospel is about transformation into a new creation; the world has no power to make itself new without Christ, so it has to rebrand corruption of the soul into a counterfeit form of transformation. And of course that creates suffering, either for them, or once they have completely surrendered to it, it creates suffering by dividing them from everyone who disagrees and inflaming the social discussion. "The soul is a wonderful servant but a cruel master"
However, when believers respond with a bad attitude, they make the truth harder to accept, and that attitude is coming from their soul too, not from the love of God. God loves these people. If we want to see the world transformed, we must also be transformed to love these people like God does.