Well, yes, because if they acknowledge that truth exists,
it can easily, logically, be proven that they don’t have it in their belief systems.
Better to believe that there is no absolute truth, and that two contradictory things can be true at the same time. Actually had a lefty say that to me, because she knew I’d be able to logically disassemble her entire belief system otherwise.
I've had that "argument" stated to me, too. When it happens, just point out that arguments don't exist in hyperspace - they are put forward by people. Therefore, when a lefty says "objectively" "there is no absolute truth, and that two contradictory things can be true at the same time" observe that that is their, personal, subjective opinion, and that it is not objective because there are other opinions about the same subject. Then tell them that you would like to hear their justification and defense of their personal, subjective opinions that they are labelling "objective."
Then step back. Because it will NOT bother them that they can't to defend their positions, or that they are being hypocritical. But the idea that their declaration of objectivity is a subjective opinion stops their minds cold. So to protect themselves, they will go into a rage at your "accusation" that they have a personal, subjective opinion AT ALL. For that is the one thing that truly, deeply frightens a liberal - falling out of groupthink, or not being perceived as loyal to it. That is their core terror, and what they punish amongst themselves most severely.
Buy some popcorn, and try it.