Archer and Shirou: NOT the same person

I disagree with anyone who says, "Archer and Shirou are the same person" and view them as the same person.

It's important to note that Archer, while being the same identity as Shirou, isn't the same person.

None of us is the same person we were ~20 years ago.

Archer and Shirou had the same starting point but their paths diverge. Shirou in UBW is very unlikely to become Archer.  He has been gaining experiences that Archer did not - thanks to the people he got to interact with and the character growth he had - and vice versa: Archer is a Shirou that's evolved over years of experiences and trauma. Their personalities are so different now that they should not be considered "the same person" anymore.

The 17-year-old Shirou is in love with Rin and probably will for all his life. Archer, however, is not and will not. Likewise, Rin is not in love with Archer because he is not "her Archer".

There's a reason that the law would not hold you accountable for a crime that was committed while you were having a mental illness or dementia.
There's a reason that the law would not hold you accountable for a crime that you committed a number of years ago.

IF your grandfather, in his 90s and suffering from dementia, pointed at a picture on the wall of himself as a six-year-old, he would say, “That’s me!”  He was right. But those two people had nothing in common. Physically, they were vastly different - almost every cell in the six-year-old’s body died decades ago. As far as their personalities - we can agree that they wouldn’t have been friends. And they shared almost no common brain data at all.

But remember - it’s not only about similarity but also about continuity.  As an old man, he knows about himself as an 89-year-old, and that 89-year-old knows a bunch about himself as an 85-year-old, and so on. Therefore, Archer and Shirou are not the same person because Archer - despite being older - does not have access to Shirou's 25-year-old self and so on. And the 80-year-old Shirou does not know about the years that Archer has spent as a Counter Guardian, either.

What most defines us as a person is memories which are shaped by our experiences. We use the word "I" to refer to our history, our past that we have access to. We have memories that link us to who we were in the past, but even our interpretation of those memories change as we change, without even realizing it. Even if for some reason, you lost all of your memories, your body would still have the same DNA that your younger self did. However, you would not be "the same person", the same "I" anymore because you would no longer have access to your past memories.

If you somehow could transfer all your brain data into a computer, then that computer IS you - even if your body died.