cavediver will give you an actual accurate answer pretty soon I bet
In the meantime it is my understanding that what GR does is to imply that the universe is infinitely more likely to be either expanding or contracting than staying still. As cavediver mentioned already, Einstein hated this, he wanted a steady-state universe, so he tried to fudge the math.
But really it's pretty simple, imagine a steady state as a point on a line with expanding being that infinite distance to the right and contracting being that infinite distance to the left. Obviously one or the other will be much more likely than that little point. The reason that it is GR that opens this can of worms is because it's the first real-world use of the idea of space that can be thicker or thinner, as it were. Once it CAN do it, what's to stop it?
But it's actually Hubble who produced the red-shift information that implied that expanding was what it was doing. From there it's a short leap backwards to the singularity, the singularity is just a point where the math has to stop. A careful study of the conditions that would have had to prevail shortly AFTER the singularity produces ideas like inflation and predictions like the Cosmic Microwave Background.
And the CMB turns out to be exactly what was predicted. Ergo, the theories aren't moonshine anymore, people have to start fleshing them out.
* Geez, how wrong am I?