Where's the logical fallacy? There isn't one.
You may not agree with the sums or the boyfriendliness of not wanting her to stay for free on a regular, obligatory basis after accepting a job in his area.
However, we don't what the facilities or his circumstances are. The OP dripfed the fact there had been a rental setup until recently. We don't know he doesn't have another in mind at some point. We don't know the going rate of the room.
We aren't in a position to assume he can just as simply take on another renter with the OP in place. I and a lot of friends have house shared, rented and had lodgers over the years and seen first hand a lot of examples where very similar situations have had big implications.
You don't have to agree with me at all. Zero interest in that. But out of interest, what's the logical misstep here in the absence of other detail? All we know is that it may not be romantic he has good potential reasons for not wanting to make this commitment for free.
I wasn't saying she'd sleep apart. The point is having another person around can affect the balance and the attraction of the place for a renter. This may be a very pertinent factor for him.
Nobody has said really why she should be entitled to stay for free when he's not happy with the arrangement for whatever reason? She doesn't have to like it but it doesn't necessarily make him a bad person or a mercenary.