I can think of 3 solutions, though (2) and (3) make some additional assumptions:
The puzzle question does not mention that the 2 scholars agreed with each other on the first two statements ("A and B are twins" and "A and C are twins"). So we may assume that the scholars are discussing 3 different entities, A, B and C, and that whether 2 entities are "twins" in their subject of expertise is not a straight-forward to infer (so they are still hypothesizing), or alternatively that concept may have been poorly defined and so is subjective. The 2 scholars are researching the relationship between the 3 entities and currently they both agree only the relationship between B and C, but differ on the relationship between A and the remaining two entities.
A, B and C are 3 conjoined infants, with A and B being joined together and A and C being joined together at birth but B and C were not joined. The scholars specifically meant "conjoined twins" when they said "twins". The scholars may be anthropologists studying abnormal birth conditions.
The scholars are architects discussing tall building structures. A, B and C are a sequence of 3 connected similar towers. A is the middle tower that is connected by bridges to both B and C, but B and C are not connected directly to each other. The scholars consider 2 towers to constitute "twin towers" only if they are right next to each other and perhaps also require them to be connected to each other directly through a bridge.