It's ok to resign, but fighting on might be worth your while
In many of your games you will, at some point, find yourself in a losing position. Whether you botched the opening or made a tactical error - facing a losing position basically leaves you with two options: you can give up or somehow try to fight on.
Why give up?
There is no shame in resigning. In fact some people might even argue it's disrespectful not to resign in a clearly losing position. Giving up also might save you some nerves. Instead of painfully clinging on to a hopeless position, you can go straight to the analysis board, look at the mistakes you made, and move on.
However, apart from the fact, that you still might turn the game around - a game is only lost, when it's lost. Losing is not lost. If you decide to play on, you might, after a while, find yourself developing an edge, that not too many players have.
Why play on?
First of all, when you decide to play on, you should be ready to suffer - quite a bit. Even in seemingly decided positions, games can go on for a while and chances are, you will probably still lose the game in the end.
But: in the process you will learn things, you won't learn better anywhere else. It will take time, but slowly you will get better at spotting any hint of a resource in your position, any hint of a threat you might have, any tiny little way to put pressure on your opponent. You will learn how to avoid simplification, how to keep the position complicated and how to use the clock as a weapon. You will find new ways to create an attack out of nothing, or how to manufacture surprising perpetuals. You will get better and better at withstanding pressure and keeping up your resistance as long as possible.
These things will not only help you to save the occasional (half-)point in a losing position. They will help you in winning positions as well, as you will also get significantly better at recognising your opponent's resources and potential threats. And: how to avoid them.
Conclusion
There is nothing wrong with resigning a losing position. But if you, at least occasionally, decide to keep on fighting, even though it might be painful and frustrating at times, ultimately it will make you a much stronger and more resilient player.
