I would agree with Roberta's interpretation in that all members of all 3 roads, are at least benefited by the main road (call it Road A), thus 3 signatures from any of those parcels is sufficient. The argument could then be would a parcel on Road B be benefited by Road C or a parcel on Road C be benefited by Road B? Undoubtedly, if parcels on Road B or C must use Road A, then they are all benefited by Road A and those three signatures you collected could have at the very least legally formed a road association for Road A.
If Peter's suggestion of developing some language that includes Road B and C as part of "the private road" fails, then you may need to form three separate road associations: 1) for Road A which includes all parcels from Road A, B, and C, 2) for Road B which includes parcels from Road B, and 3) for Road C which includes parcels from Road C. Forcing owners from Roads B and C into two separate road associations might be enough to convince the owners fighting the matter to accept all roads as part of one association.
Our association has 2 roads. One of which has 2 parcels and only those parcels are benefited by that road. Our lawyer drafted up our documents to include both roads in our association. And provided for the future in that the event that the larger main road dissolve the association and become a public road, the 2 parcels on the smaller road could remain as an association of 2 without any of the others being included. We were fortunate that nobody fought this and every agreed.