You should never resign just because your opponent wants you to, but you should resign when you objectively decide that you have no way to save the game. After the conclusion is inevitable, you may as well shake your opponent's hand and go your merry way.

Is it rude to resign in chess?

Resigning a move or two before certain checkmate is actually a mark of disrespect, as it removes the opportunity for your opponent to make the killing blow.

How do you resign in chess?

On the web page, look to the right of your game board, just above your user name. Click on 'resign' next to the white flag, and the game will be ended, and you can start a new one!