There wasn't a small chance, there was no chance period. He knew that, but didn't want to accept it. He wasn't betting all in an off chance, he was deluding himself into believing there was a shit chance in hell of making a difference at that point, even though there wasn't. At the same time, in his bitterness, he rejected everything that lead him to what he was and discounted the chance that just maybe he could have solved things better. Hence why in HF, the one ending that has Shirou going the Kiritsugu/Archer route is a Bad End, Archer and Kiritsugu's coldblooded heroism didn't do anything but make them miserable.
Once again, the whole point of the UBW battle and the meaning behind the Unlimited Blade Works incantation: A person who wishes to do something that is not possible while being aware of that, yet doesn't let up in his efforts. Cue Archer's sudden "Holy shit, I was really like that? That's pretty cool."