Why is seahorse not a good scientific name?

A major reason is that "sea horse" actually covers multiple different species of animals living in many different habitats. A scientific name needs to be specific to one interbreeding population of animals so that information about that species can be discussed without confusion.

Put another way, using "sea horse" as a scientific name is about as useful as talking about "rocks" in geology - there are so many different things you could be talking about that a scientific conversation is not possible without further defining what exactly you are looking at.