The irregular nature of "to be" in English comes from it being a blend of three different roots with a somewhat similar division you're talking about (but certainly not as clear, division was more about tense than duration).
The fallacy you're talking about I consider a specific instance of the labeling problem. If someone is marginally in a group and you apply the label of the group on the individual, suddenly it seems ok to use attributes of the group to reason about the individual. One jumps from specific to general and back to specific again without acknowledging the loss of information from the abstraction layers. Often comes up in post hoc rationalisation of harsher criminal punishment, for example. John is a criminal; we need to be tougher with criminals; therefore we need to be tougher with John - without regard for the specifics of John's case.
The fallacy you're talking about I consider a specific instance of the labeling problem. If someone is marginally in a group and you apply the label of the group on the individual, suddenly it seems ok to use attributes of the group to reason about the individual. One jumps from specific to general and back to specific again without acknowledging the loss of information from the abstraction layers. Often comes up in post hoc rationalisation of harsher criminal punishment, for example. John is a criminal; we need to be tougher with criminals; therefore we need to be tougher with John - without regard for the specifics of John's case.