I still cannot full comprehend the essence of a critical point on phase diagrams. 

It is usually said in textbooks that the difference between liquid and gaseous state of a substance is _quantitative rather than qualitative_. While it is easy to understand for a liquid-solid transition (symmetry breaking is a qualitative change), it is unclear to me what meaning does it have for a liquid and it's gas.

1. is it correct to say just "this substance is in gaseous state"? Shouldn't we also specify the path on the phase diagram by which the substance got in it's current state - did it cross the boiling curve or went over the critical point and never boiled?

2. why does a critical point even exist? Blindly, I would assume that either there is no boiling curve at all - since the difference is qualitative the density of a substance smoothly increases at all temperatures and pressures; or that the boiling curve goes on to "infinity" (to as high pressures and temperatures as would remain molecules intact). Why does it stop?