When Walking Away Feels I'm Giving Up

Regardless of the server, when things get too tense for me on TF2, like someone able to get headshot after headshot to the point that they may be suspected of using an aimbot, or just seems like I can't do anything right no matter what, I find it trouble for me to walk away and do something else. Reason is that if I quit I'll feel like a quitter and that I'll be letting those players get to me of being nothing but a failure, even at the end when it gets fun and more relaxed. I'm probably too full of pride to swallow and cut my loses. Just... hate being showed up like that one after another and that I'm just pathetic in anything, regardless of how I'm progressing. 

On the new server I go to, there's this player that is stupidly unbelievably good at sniping. One headshot after another after another, no hesitation what so ever from this guy. It's very aggravating to me and I'm sure to other players. First day on that server for me I was happy and having fun, next day can't make two steps out of spawn without getting headshoted instantly.