well, there can be all sorts of reason.
Platforms somewhat count as solid blocks, so, in the right room, the row of platforms cut the room in two. the room below (with the furnace) is obviously too small, and the room above have no actual solid blocks floor, which an NPC could be standing on. they requite I think at least 3 (or is it just 1?) solid blocks to stand on the night. That room has no solid blocks at all as its floor.
it also can be furnitures in the way, as I said. - maybe also multiple factors at once.
It also can be that an evil biome is close by.
and I think I read about some bugs (but it might be only on PC) where NPCs don't like special shapes of houses. I dunno if it's about that, but a more "normal" shaped house probably would work without problems. but if you prefer this shape, then I guess it might be something with the floor.
Make sure that the floor is solid blocks (at least 3) and that not the whole floor is covered in furnitures. (if you put the table and chair on plaforms of a single row, I think it will cut the room into two rooms, so, with this method, I think the table (workbench) and chair should be on separate platforms, not in the same line.
But it is possible, that the problem was just the lack of solid blocks floor, and not the furnitures being in the way.
At least on PC, (I don't have a mobile device.) In a 3x10 room, which is the smallest size a room can be when three blocks wide, at least one of the floor blocks needs to be a solid block and not a platform. I usually put it in the middle of the two platforms, and you can walk beneath that floor to talk to the NPC. Or from the side. However you want to do it.
... not that I can see what's behind that white "2" or slime that might possibly be hiding what could be either a single block or a wooden platform.