When we see ourself in others, they stop being "others" and become "us"

I watched “How to Train your Dragon” yesterday and was moved by this exchange:

Astrid It’s a mess. You must feel horrible. You’ve lost everything.
Your father, your tribe, your best friend…
Hiccup Thank you for summing that up.
[silence]
Why couldn’t I have killed that dragon when I found him in the woods?
Would’ve been better, for everyone…
Astrid Yep. The rest of us would have done it. So why didn’t you?
[pauses]
Why didn’t you?
Hiccup I don’t know… I couldn’t.
Astrid That’s not an answer.
Hiccup Why is this so important to you all of a sudden?
Astrid Because I want to remember what you say, right now.
Hiccup Oh, for the love of… I was a coward! I was weak! I wouldn’t kill a dragon!
Astrid You said wouldn’t, that time.
Hiccup Agh, whatever… I wouldn’t!
Three hundred years, and I’m the first Viking who wouldn’t kill a dragon!
[pause]
Astrid First to ride one, though.
So…?
Hiccup I wouldn’t kill him, because he looked as frightened as I was.
I looked at him… and I saw myself.