Not all arguments are equal. If you are arguing how magnets work, it is clear-cut. There is one correct answer. If you start arguing something like whether or not slavery is a good thing, it becomes less simple.
Slavery is a terrible thing. Humans are born free, with free will, and they should never be forced to do anything they do not wish to do.
Slavery is a wonderful thing. It is a long-standing tradition of humanity and it has yielded truly spectacular results. The greatest wonders of the world were created on the backs of slaves. Therefore, slavery is a collective effort (one of the great traits of humanity) that creates long-standing greatness.
Both of these points are correct. Both of the people truly believe the things they say. The difference is values. The first person believes that the most valuable thing is for a person be able to choose their fate. The second person believes that the most valuable thing is the results of work.
It's nice to think that all problems can be solved, that all differences can be settled. But when the differences are in values, that just isn't always possible. Sometimes the best hope is to agree to disagree, but we're not all capable of doing that, either.
The one nice thing about it is that you can get a hell of a story by trying to get people to express their values and convince other people that those values are valuable.