This is flawed reasoning and I'll explain why by analogy. (Side note: I don't mean that an analogy is proof of anything, it was just the simplest way to explain how I think on the subject of the grandfather paradox and similar)
Let say you put a ladder up against a roof and climb up. Once up, you push the ladder over. Even thought there's no longer any way to get up on the roof, you are still there.
Now think of the ladder as the chain of events that led to your inventing time travel/going back and the roof as the act of saving your loved one.
Even though there's no longer any need to time travel and save them, you still did.

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