Divide The Space
If you have a single largish territory for one group, you need to be able to divide it into two or more pieces in order to live. That gives you your two eyes. Note you don't have to do this to live; but you have to be able to. If there's only one way to do that, then chances are there's an obvious way for your opponent to stop you. Which is bad, because then your whole group dies. (Generally. The outside of your group has to be surrounded by living groups for that to be true, or at least by groups that can be made alive before you can escape; otherwise you get things like semeais. Life and death is complicated when there are still a fair number of liberties around.)
Playing at the vital point of your big eye divides the space. Your opponent playing there prevents you from doing that. Such a move needs no follow-up. Liberties don't count anymore unless you can capture something else to live.
So be careful. You might think "I have six points of territory here; it has to be good for two eyes, and anything my opponent puts there must surely die." You might not even think of such a play.
You might be wrong.