I Google'd to see how many results I could find about Finn not being Human, and got about few hits lol. But not much to counter them.
Anyway, people on the Wiki (and outside) are convinced that Susan Strong is Human. I have yet to see a comment on here about Finn being a Fish Person. In the episode "Beautopia", Susan was surprised to see Finn had no gills, of course the ending seems to nullify this. But what criteria makes a Homosapien in the Land of Ooo?
In the episode "Her Parents", Bob and Ethal thought Finn was a goblin. Even though from what we've seen, Goblin skin is various shades of green and their anatomy is obvious. But to counter this you can say their nearsightedness contributes to their Goblin!Finn statement.
So what if Finn is a subspecies of Fish Person, and as a result was abandoned because of it? If anyone here has watched Futurama, and remember the episode about Leela discovering her real parents are subhuman (mutants) and thus not making her a alien-cyclops, the theory becomes a bit more clear, lol only it is in reverse. So lets think about the episode "Memories of Boom Boom Mountain", and baby!Finn crying stuck to a leaf; as a toddler there is no way he could have taken care of himself while out in the middle of the forest. However, to counter the abandonment theory, perhaps he was like the Jiggler and wandered away from his care taker, becoming lost but got lucky when he was found by a species that loved him.
On a miscellaneous note, in the episode "Ocean of Fear", Finn discovered his phobia of the ocean. He had no issue with other bodies of water. Now, when you think about the ocean, and the 'beginning of life', there are a lot of people who like the idea that humans and just about everything on the planet came from the waters, namely the ocean. Perhaps Finn had a deep fear because as a toddler, he nearly drowned due to his lack of gills.