For those that are not familiar with this phrase, throwing in the towel is what they would do in boxing when either the fighter or the people in the corner of a fighter felt like he couldn't take it anymore. They gave up, they surrendered, they quit. I am telling you, don't give up, don't surrender, don't quit.
You have started down a path that you chose for yourself. You decided to start a new business, or go back to school, or challenge yourself to loose weight, get out of debt, play an instrument, learn a new language or something else. What I am telling you is stay on that path. It will not be easy but it will be worth it. You will have days when you feel like it is not worth it. You will have days when you ask yourself "what made me think I could do this?" You may even have days when you just break down emotionally want to "throw in the town." I am telling you stay in the fight. There is a scene toward the end of the movie "Creed" when Rocky was going to throw in the towel because was beat up pretty bad. Rocky felt bad because he didn't do it for Creed's dad, Apollo and he got killed. Creed told him not to throw it in. Rocky asked him why and Creed said because he wants to prove that he wasn't a mistake. (start at 2:31 in the video clip)
That is the mindset that you need to have. Don't give up because you starting your journey, whatever it may be, was not a mistake. You had a vision, dream, desire in your head and heart and you decided to act on it. That was not a mistake. You wanted to achieve it, that is not a mistake. You may get knocked down, beat up, the people around you may feel like you should you give up but don't you listen. If you believe in your journey don't let anyone knock you off of it. You never know, your "not going to throw in the towel" mindset may rub off on someone else. If you are familiar with the Creed movie, you know that as soon as Creed said he wanted to prove he wasn't a mistake and he wanted to fight, they inspired Rocky to fight as well. Rocky has Cancer and although he was taking treatments he wasn't giving it his all. He was actually doing it more for Creed and than himself. When Creed made his statement it gave Rocky the desire and drive to do it for himself.
The only mistake for you would be not following through. If you quit you will live forever with the "what if" for that thing. That it truly worse than not succeeding at something. If you don't succeed or get the results that you wanted, you know that you tried and that you can try again and do something different than you did before and see if that works. If you give up all you proved is that you don't have the drive to finish. And just like Creed inspired Rocky, you can also be setting an example for those around you. You never know who is watching you. Remember the main person you need to prove this to is yourself. Others will be inspired by you... to keep trying or to throw in the towel. It's on you.