Because it is (Kind of) a Dragon
The Crabby Nook claims that chinese cultures believe the Seahorse to be a type of seadragon.
However, they offer no sources, so I can't really believe that.
This site corroborates Meta Ridley's answer:
According to some legends a seahorse is a baby dragon, and thus
seahorses are often tied to dragons. Like Dinosaurs Are Dragons, this
is largely an Eastern culture trope: most notably, the Japanese word
for seahorse, "tatsu-no-otoshigo", literally means "dragon's ...[illegitimate]...
However, none of this really matters. I could find no proof of anything. This "legend" the Crabby Nook mentions was highly elusive. The only thing on Chinese seahorses I could find was their use as powerful medicine, and Japanese seahorses are definitely not dragons.
It seems to me that this leaves one possibility.
Sea dragons are very much related to Seahorses. They are in the same family, and have similar attributes. They do have one notable difference, however. Seahorses are highly mobile, while Sea Dragons just drift around.
That means Horsea is definitely a Seahorse, not a Sea Dragon.
If attacked by a larger enemy, it quickly swims to safety by adeptly
controlling its dorsal fin.
Based on this, I think Game Freak created a compilation Pokemon.
Horsea isn't based off only one thing.
But does it really matter? It makes for a pretty sweet Pokemon.
Personally, I'm O.K. with them getting it just a little wrong.