Because if mass were infinite, you would have enough of it to fill every nook and cranny of the universe, no matter how big the universe was. Otherwise, it would mean that mass is "less infinite" than space.
Hello. The word "infinity" often comes up in physics, but observational evidence seems to preclude any form of infinity whatsoever: either everything must be infinite, or nothing can be infinite.
My line of thought comes from the fact that the density of our universe is not infinite. Therefore...