Shanks and Luffy thought...
The gum-gum fruit being an mythical one instead of a paramecia explains a hell of a lot why Luffy is a constant on Shanks's mind after so many years.
I mean, I get it. Luffy was an adorable kid who idolized Shanks and saw him as a father, but Shanks is a veteran world traveler and a seasoned warrior.
There was NO REASON for him to lose his arm to a Sea King for Luffy. There was NO REASON for him to panic so badly that he forgot his conqueror's haki and plunged into the sea to save the kid. EXCEPT--
Luffy had eaten the Gomu-Gomu no Mi which was actually the Mythical Zoan fruit the Government was trying to hide so that the events of the Void Century never repeated themselves and so that they could retain all of their power.
Luffy had eaten the fruit the WG was so terrified of to the point where they had an entire division of Cypher Pol transporting it, a team that Shanks defeated for the sole purpose of retrieving a fruit that his Captain had told him about (in theory, because Shanks was a good soft boi who took care of his brother instead of going to Raftel).
The FRUIT was in danger of being lost to the whims of the Sea once again and there was no way Shanks could predict where it would turn up again - and what if he couldn't find it before the WG did?
I adore Luffy, and I adore Shanks, and I adore the relationship they have, and I truly believe that over the years Shanks truly came to love Luffy the same way Roger did him and Buggy, but a part of me believes that it was the rubber fruit that had him panic so bad, NOT Luffy.
Shanks had been a pirate since childhood. He traveled with Hiyori and Momonosuke. He's met, played with and said goodbye to many children over the years. The world he lives in and grew up is cruel. Hell, he saw Tequila Wolf up close and the little we've seen through Robin's eyes showed us there is likely a lot of young deaths happening there.
But the ones he is so close to, the ones he considers his children (hello Uta - I still don't know how I feel about your existence and until I see the movie, I won't be figuring it out) are the ones that have close ties to the WG in some way. I simply can't reconcile Shanks's complete loss of control over his emotions and abilities simply because of a child.
A child with a mythical ability to turn the WG on its head and change the world on the other hand? Yeah, I'd panic too. And I'd keep close tabs on said child if only to know when to pull up stakes and disappear before said child begins breaking the world apart.