One way to see this is to consider the clock paradox. Spaceships A and B are moving about 86% the speed of light relative o each other. Spaceship A look at B and says the clock at B has slowed down by half. Time slows down for moving objects. But B says no, they are not moving, A is moving. So B says the clock that the clock at A is the one that has slowed down by half.

So how do we test who is right? If A goes and parks next to B to prove they are right then B would appear to be right. But if B goes and parks next to A to prove they are right then A would appear to be right. “Now” is not any more universal than up and down.