What I got out of it:
The Butler's son leaves home, runs into Skull Kid, and gets killed. My guess is he was killed by being turned into the tree, not the other way around. SK finds Link and turns him into a Deku Shrub using the soul of the Butler's son.
I think everyone excepts the fact that the tree is the son of the Butler, so I'll skip that.
Why doesn't Tatl just tell Link? They just met and she and her friends killed his horse (I think the Epona in MM is a different horse. Every character in MM is a recycled one from OoT so it only makes sense that there'd be another Epona) and turned Link into a shrub. Despite this, he is still willing to help her after SK abandons her and she's probably feeling somewhat guilty now. When they see the twisted tree she wants to confess, but she can't just say, "Oh look, the Deku we killed to turn you into this.", he's the only one who can help her.
Instead she says that they look alike. Everyone in LoZ (including just about every player, as they were in OoT) is familiar with Deku shrubs so it doesn't makes sense that she'd say that just to point out that they're both shrubs.
Why can't you take off the mask? I haven't gotten to Great Bay yet, but I know you create the Goron mask by soothing Darmani's soul with the song of healing. Same thing with the Butler's son. You sooth his soul with the song of healing and create the Deku mask. The only difference is that Darmani is a ghost who you knowingly help while the Butler's son is trapped in you who you accidentally help by trying to cure yourself. You can't take off the mask, because there is no mask, not until you learn the song of healing.
The Butler says his son left a long time ago, but if the theory's true then he just died, how is that possible? Just because he died just before Link met Skull Kid doesn't mean he left just before they met. He could have explored all of Termina before being killed by SK.
Reasons I think it's the Butler's son:
Every other mask has a soul, only makes sense the Deku mask has one too.
Tatl says they look similar despite the fact that all Deku shrubs look almost identical (other than those then player needs to be able to recognize, i.e. the King, Princess, Butler) hinting that there's either something about them or she knows something.
The Butler says Link reminds him of his son. The other masks make Link look like those who's souls made the mask so it makes sense that if this mask made Link look like the Butler's son then his soul was used. But then why doesn't anyone else recognize him? The Zoron mask is made with a member of a famous band and the Goron with Darmani who's obviously famous amongst gorons, but the Deku is just the Butler's son so the fact that the others a commonly recognized, but the Deku only by his father makes perfect sense. Who's going to remember the Butler's son who ran off years ago?