"It seems like you can replace any component of a ship, and it is still the same ship. So you can replace them all, one at a time, and it is still the same ship. However, you can then take all the original pieces, and assemble them into a ship. That, too, is the same ship you began with."
Let's use this as a metaphor, shall we?
If the 5 year old me looked at me right now, she would probably be shocked. Actually, if the twelve year old me saw me, she would be shocked too. Because we change as we grow up, and we keep changing. If I get to 80 years old, how much will there be left of the 5 year old me? Maybe not much (hopefully a lot). So, am i still the same person? If every piece of me was slowly replaced with a new one - every feeling, every opinion, every habit - am I still the same ship?
Now, here's why we can't compare ourselves to ships: what binds all the versions of ourselves together is what we've gone through, our memories; they influence the way we act and they transform us - we could never be the current version of ourselves if we hadn't been the old ones.
That's why so many books and movies like to explore the idea of amnesia (especially extreme cases). Weather you are a star crossed lover or a post apocalyptic hero who has their memory wiped off, what you've been through is who you are. And when you can't remember where you came from or what you like and who you love, you turn into a blank canvas, you are someone new. When we wipe your memory away, that kid you pushed off the slide when you were 7 can't blame you anymore, because you simply stop existing. He can only blame who you used to be.
You can have someone who is exactly like you: they love the same things, they share every opinion with you, their tooth brush is the same color and you guys both wake up at 54 seconds past 7:48 AM. You have all the same pieces, like a ship, and you still aren't the same person, are you?
I read somewhere once that the human mind is one of the most complex structures in the universe but not complex enough to understand itself. Life is fascinating on its own, but human life, within all its greatness and terribleness is remarkably wonderful. We can't be sure of most things, not even of who we are, but we certainly know why we are this person, and after we realise that, we can choose to continue too be that version of ourselves or we can choose to change and still be the same person. I guess the lesson here is that people aren't ships.