I would have argued the same thing, but @dwinblood makes a good point about perception. The facts are reality. Someone with perfect perception and integrity would know the absolute truth - but no one has perfect perception and integrity.
Necessarily, because we are imperfect perceivers, and less than perfectly honest about what we perceive to ourselves, we must have a subjective truth, each and all.
This does not mean we are lying. Merely that we each and all are incapable of knowing the absolute factual reality, and thus each of us knows an actual different truth that we perceive to be reality.
We cannot claim to know the absolute truth, and thus must, if we are honest, acknowledge that other's truths are necessarily different than ours. Facts remain obectively real, yet we must perforce disagree - at least in part - honestly about what the facts are.
Factual reality, this absolute truth you speak of that none of us mere humans can attain, is objectively real. We mere humans can only approach that reality more or less closely, dependent on our subjective experience.
While your truth may be that you should kill 10k people, that does not mean we need to agree with you, nor allow you to do so. People can reason and discuss from their disparate viewpoints, and come to accommodations mutually acceptable. Preferably that do not involve killing people.
That ability to reason and accommodate is what separates us from psychopaths. How many times have you acknowledged that someone whose viewpoint differed from your own had a point, because you understood a point they made that changed what you thought of as truth?
There you have it, Truth and reality are different sides of a coin. Man can't see the truth. We can only have a perception of what we might think it is.
Just by claiming that truth is relative we could cause harm to our society if everyone has a truth, automatically everyone is right, therefore concepts such as good or evil would be extremely relative.
There are universal concepts that goes beyond human understanding.
2 + 2 = 4, that's truth.
Gravity is truth.
Yes, you are right, but we could try to reach it we must follow towards the absolute truth because it is there and we know because of the Facts that absolute truth is real. If facts wouldn't exist, the absolute truth wouldn't exist too. Facts are the tools we use to ascertain that truth exists and we can reach it somehow.