Opposition

Hi. I have a question. Recently, I was doing Lichess practice and I got to one about opposition that looks like this.

As far as I am aware, Opposition reffers to when a king prevents another king from intruding on a certain square, usually when they're on the same rank and 1 file separates them, or on the same file and 1 rank separates them. Lichess says h4 is winning, while g4 blunders a draw. (Any other king move not on the 4th rank allows black to take the opposition on the 5th rank, and any pawn move is just atrocious). H4 doesn't move closer to the pawn, while g4 does that and maintains opposition, because if black wants to get closer he has to play g6. So why is it that the slower looking move wins?

What I mean to say is, g4 get's to the pawn faster, allowing you to take opposition faster, but it draws, while h4, which allows you and your enemy king to get to the pawn faster is a win. How?

This is actually trickier than it may look.

1.Kg4 COULD have worked, but...

I don't understand what you mean by "get the opposition faster", it literally gives the opposition up, you'll never get it after that. Well, you could if not for b3 move.

Here's a simpler example

Here 1.Kh3 wins and 1.Kg3 draws. And in your original position, if we remove the black pawn, both 1.Kh4 and 1.Kg4 win. Is all this clear to you?

I appear to misunderstand how opposition works. I know the fundamental concept involves the two kings preventing eachother from moving to certain squares. However, if we try to be faster and get there first, we get to the pawn first and black then gets the opposition, because whenever he moves, he'll move to limit my king. If I allow black to get there first, then i'm allowed to set up the opposition. Is that correct?

Getting anywhere faster has nothing to do with it. The point is you must have the opposition when you get whenever you wanna get. Opposition is not something you can set up at some point, you either have it (and then you won't lose it) or you don't (and then you won't get it) - at least in these positions. In more complex cases it gets trickier, but for now try to grasp the idea for these simple ones.

If white is simply able to take the pawn on b4, it doesn’t make any difference what square Black’s king is on, (assuming he can’t take your pawn of course) it will be winning for White regardless, as he will always have the spare tempo move with his c-pawn. 

But because Black can force white’s pawn to move with the …b3 sac (as was already pointed out) you can’t guarantee having the spare tempo as mentioned above. 

For example whites pawn on b3, White king on b4, black king on b6: white needs for it to be black to move, that’s why you have to start with 1.Kh4.

This is more about critical squares which are b4, c4 and d4 if black does not capture the pawn and b5, c5, and d5 if black does capture white's pawn. Opposition is one means of occupying a critical square.

The thing about taking the opposition is that it basically putting your opponent in zugzwang. Your opponent must move first, and you knowing what your opponent did can take a key square that he/she forfeited if beneficial, or else just take the opposition next turn and your opponent will have the same problem.