Absolute truth does exist. In "true" science, there are many scientific laws that illustrate there are some absolute truths. As humans, we would not be able to function in a world filled with relative truth. In order to function and interact with each other, we need some portion of absolute truth.
When everyone has their own truth, by logical extension, there is no truth, since truth in that mindset all depends on the person's perspective. In societies filled with relative truths, relationships and society quickly fragments.