Fallacy of composition
The fallacy of composition is a logical error in which one claims that because the parts of a whole have a particular attribute, the whole must also have that same attribute.
An example would be the claim that because everyone in a particular town has a younger sister, then the town also has a younger sister. A town cannot have family relationships even though all the citizens of the town have families.
A different version of the fallacy would be to say that because all of the individual parts of an engine are properly constructed, it follows that the engine as a whole is properly constructed. In this case, the interactions between the individual parts introduce a new level of complexity and possibility for error above and beyond that which applies to the individual parts.
In economics, the fallacy of composition explains the benefits of division of labor. An individual worker may benefit by specializing in a particular task, but it does not then follow that the economy as a whole would benefit if every worker specialized in that same task.
The inverse of the fallacy of composition is the fallacy of division.