Why is this a loss?

I'm white, my turn, I moved to c3. Why is this a stalemate and why don't I win? He can't move up, and he can't move towards my king. Pls help.

It's not a loss.  It was a draw by stalemate.  Stalemate occurs when it is a player's turn, the player has no legal moves, and the king is not in check.

In the position you posted above, note how your opponent only has a king.  The king has no legal moves, and he is not in check.  Therefore, stalemate.

More examples and explanations in this official article: https://www.chess.com/terms/stalemate-chess

The guy with the beard's talking nonsense. How does stalemate give the opponent 'big chances'?

Thank you. And lol at the beard guy. Useful to know.

Can the castle swap with the king? I saw this happen in a game and was confused.

It is not a castle, it is called a Rook.

And CASTLING is the move you are referring to, and it is NOT a King and Rook swapping spots.

Castling is moving your King 2 squares TOWARDS one of your Rooks on the back rank and the bringing that rook to the square neighboring the king on the opposite side of the King.

For example, if White castles Kingside, his King moves 2 squares to g1, and the h1 rook goes to the other side of the King on f1.

In order to legally castle, ALL of the following MUST be true:

1) The King has not moved yet for the entire game.  Move the King even once and castling rights are lost.

2) Whichever rook you are castling the King with must not have moved yet (the other rook can have moved)

3) There are no pieces, Black or White, currently between the king and the rook that the king is castling with.  So if Black wants to castle Queenside, nothing Black nor White can occupy the b8, c8, or d8 square.

4) The king cannot castle out of check.  If you capture the checking piece or interpose the checking piece and do not move your king, you might be able to castle next move.  Move your king and castling rights are lost for the rest of the game.

5) The King cannot castle over check.  This means for say, the White King to go from e1 to g1, the f1-square cannot be controlled by a Black piece, like say, a Black Bishop on a6 with no other piece or pawn on the f1-a6 diagonal.

6) The King cannot castle into check.  There is no legal move where you can put your own self into check, and so castling is no different than a regular move in this aspect.

So no, in that stalemate example by the OP, White cannot castle.

Well, when you have a bare king, getting a draw is the best chance you have, since there is no king only checkmate. 

     You win chess games by checkmating your opponent. In the diagrammed position, it is black's move, but he cannot make any legal move. There can be no more moves made in this game, so it is over. Yet white has not checkmated their opponent, so they have not won the game.