Background: When Shirou was alive, he made a contract with The World to become a Counter Guardian (CG) in exchange for power to save more people. The World - aka: the Counter Force Alaya - is a Defense Force that prevents any man-made threats that would cause humans to be eradicated by themselves. As Archer explained, he has been sent to many different eras in the past, present and future to stop and clean up the messes that humans have made. What this means is that he gets dispatched to situations where mankind is destroying itself and stops it by killing the people within a certain area, generally after they've already done their damage. He was essentially fooled by the Counter Force (and himself), giving up his life to pursue the impossible goal of saving everybody.
When one becomes a Heroic Spirit or a Counter Guardian, his existence is outside of time and space. This is why, even if his past self dies, he won't be affected.
He never received anything for his innumerable times helping out humanity, which caused him to “embrace” the landscape of his Reality Marble: barren and filled with painful reminders of violent actions. His disillusionment started when he realized that although “he made lots of people happy,” the "reward" he received wasn’t his own happiness but rather “the fate of being exploited as a Guardian even after his death.”
Now, here is something that the anime does not explain: the real work of Counter Guardians: What we should know is that CGs don't empower people at all. They do not make efforts to prevent disasters, either. They "clean up". For example, if an evil overlord appeared in Japan, he could destroy the world, but CGs would only come after he had done some damage, then they would not only kill him but nuke all of Japan. They don't "save" people; they kill and destroy everything and everyone within a certain range of the disaster to prevent it from affecting the rest of the world. In summary, the Counter Force will summon a Counter Guardian, who will kill everyone involved, including the failed protagonists and random bystanders in the way. [ I believe that they should've added this information to the anime because it changes how we see Archer ].
If you want to save everyone but do not value your own life, then you're essentially exempting yourself from what you expect of others (in this case, being saved) and that is self-righteous hypocrisy. This applies even more so if someone had saved your life because you're essentially throwing away their act of saving you but you expect everyone to accept your act of saving them. The hypocrisy comes from the fact that he wants to save everyone yet he can't save himself.
If you don't want anyone around you to cry anymore, then what would you do about rapists, murderers, mafia or governments who harm other people? Would you not try to fight them in order to protect the innocent? If you want a world where everyone is happy, then you have to eliminate those who go against it in order to protect that Utopia. You more often than not have to harm in order to rescue. Considering human nature, such situations will arise an infinite number of times and the result will be that you would have to become a ruthless machine that saves only those whom it determines are more worthy of salvation. Hence, "a superhero can only save the people he has saved."
That dream is nice and selfless, but naive. Going for it with a lack of self-preservation like Shirou does is futile and even stupid. Even if I had the power of a CG, it could not be achieved. Only when I were a god who would take away everybody's free will then a perfect world without evil could be born.
In general, the ideal that Shirou follows is impossible in reality. Shirou himself admits that.
Also up to this point, Shirou's desire to save everyone is actually just a deeply ingrained desire to save himself. He thought that by following Kiritsugu's ideals, he would find happiness, and that happened to involve granting salvation to others. Archer calls it a "fake ideal" because he (and Shirou) followed it more to alleviate their own survivor's guilt. Archer never reached a definite conclusion to his dilemma, till his ideals destroyed him - it's how Shirou would turn out if he did not learn from his experiences in this war and make his own choice.
Archer followed that ideal and found out how terrible being a hero really is. He wanted to save people and be like Kiritsugu but ended up being betrayed by the very people he saved. Archer comes to hate humans and become extremely cynical because of this, and hates even the idea of heroes. After selling his soul to Alaya, he believed that after his death, he would be able to save even more, but the end result was a timeless massacre. He is now permanently trapped in his own personal hell. So, no ideal, no peaceful afterlife and lots of killing made him hate himself and his life choices, which led him to feel betrayed by everything he believed in.
It's important to note that Archer, while being the same person as Shirou, isn't the same person. Archer is a Shirou that's evolved over years of fighting and trauma. Although Archer, deep inside, still wanted to be the Shirou he was before, he learned very quickly that it would be impossible. He began to look at his ideals more critically: He hated how hypocritical they were, how naive they were, and how they were nothing more than an inheritance from a dead man.
"But still - I was not wrong."
"There is nothing more beautiful in life than chasing your ideals and pursuing your dreams. This is true for every single one of us. And inevitably much of it is lost or muddled as we age as we have to deal with the harsh realities of life. Sometimes we even silence that young voice within us that told us to keep going. All of us at some point become jaded or cynical. We tell ourselves that our best isn’t enough. That we’ll never get to where we want to be, so what’s the point?
We forget that our younger selves are always within us. Telling us how much better we are than we were yesterday. How we can accomplish so much more now than when we were that young. How dare we be able to do so much more than that little version of us but refuse because we simply believe we aren’t good enough?
"This is the battle between Shirou and Archer. One disgusted by his grown up self who has given up his dreams. The other disgusted at the naivete of his younger self." [ Archer's VA ]
Beneath the survivor guilt and the copied ideal, there is a deeper layer consisting of a dream. The dream that no one has to go through a hell like this anymore, an imagined world where everyone can have a happy ending. This is what Archer had forgotten, and it's what keeps Shirou going.
“I found my answer. Don't worry, Tohsaka, I'll do my best from now on, too.”
Archer is now at a point when he will continue to do his duty as a CG, and he will hate doing his duty, but he will continue. He may experience the pain of killing others, but he is no longer suffering this mental anguish like he used to prior to his encounter with his younger self. He still has regrets, and he still wishes to go back and do it all over again and escape the cycle of CG, but he realizes that he did not make a mistake when he pledged his life to Alaya. Archer realizes that him making the choice he did was a correct answer -- and there was no really right or wrong answer at that time. Thus he may have regrets at this time and now, but he realizes he should not have any regrets for his past actions because he sees himself in the past vs. now as two different entities.
It's more that Archer found solace in the determination of a boy who wants to become a superhero. Even when he knows that it’s impossible, that it’s futile, that he will eventually be betrayed by everyone or himself and face an eternity of being a slave, it doesn't matter. Archer realized that there was beauty to be found in the pursuit of an ideal upon seeing himself fighting to the fullest and remembering why he took that road in the first place. He realized that he cannot keep blaming himself for the choice he made when he was younger and didn't have the knowledge and wisdom that he does now.
