I can think of 3 solutions, though (2) and (3) make some additional assumptions:
Solution 1
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.
Solution 2
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.
Solution 3
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.