In chess, not being able to make a legal move while not in check is a stalemate. That's a draw, half a point.

But isn't the goal of chess to capture the enemy king? To force him onto a square where you can capture him? How is not being able to avoid stepping into check an excuse for losing the full point? After all, stalemate doesn't occur when you're winning: when you are stalemated, it's safe to assume the other player has a significant material advantage.

So why does this rule even exist? Wouldn't it be far more logical to just lose when you are forced to give up your king? If anything I think chess would change for the better. Openings would be no different, just the situations where one player has a significant material advantage would deservedly result in a faster win- no more awkward maneouvering to avoid that specific, unnatural situation called stalemate. Wouldn't this make chess a better game?

Maybe, but the rules don't necessarily have to make sense in my opinion. I think stalemate adds beauty to the game.

+1

Castling doesn't make any sense at all but its a rule.

It's actually not safe to assume your opponent has a significant material advantage. Many KP v K endgames are drawn because the lone king can force a stalemate.

The object is checkmate.  By definition the King has to be in check to reach this conclusion.