Lekhni wants to know what was wrong with Falstaff referring to the the Fallacy of Division in his post. Thinking through the Boeing 747 example in the Wikipedia article should make the problem clear. Yes, the fact that a jet plane can fly across the Atlantic does not mean that its individual parts can fly independently across the Atlantic. That is because while a jet plane is composed of its individual parts, a part of a plane is not the plane. While we can have interesting philosophical debates about how many parts one has to remove from a plane for it to cease being a plane, the point is that an engine of an aeroplane is not an aeroplane.
Contrast this with the statement “People of Lucknow speak Hindi”. Unlike the aeroplane example, one can divide the populace of Lucknow into two halves, four quarters, or ten tenths and to a large extent, any statement one made about Lucknowis will be applicable to those halves, quarters or tenths.
In fact, the statement “People of Lucknow speak Hindi” is a generalization whose truth or falsehood one can verify only by looking at the level of individual Lucknowis. If I meet a sufficient number of Lucknowis and find that most of them speak Hindi fluently, I will feel sufficiently confident in stating that people from Lucknow, in general speak Hindi. If you hear from me that most Lucknowis speak Hindi, the statement will be useful to you only because the next time you meet an individual Lucknowi, you will know which language you can start off with. I don’t see how one claim that if you do just that, you will be committing any fallacy, let alone the fallacy of division.
Of course, it is a fallacy if you persist in trying to speak in Hindi to a Lucknowi even if it is abundantly clear that he does not know the language. It is also a fallacy to turn it into a moral issue (“Lucknowis speak Hindi. You are a Lucknowi. So, you must know the language, or there is something wrong with you.) But if you treat it as an example of the fallacy of division, it would mean that if you got off at Charbagh station and found a porter who does not speak a word of Hindi, you would be committing a fallacy if you so much as expressed surprise.
What applies to Lucknowis speaking Hindi applies just as much to women supporting women’s issues. If women in general are more likely to support women’s issues, you are not committing the fallacy of division if you expect an individual woman to be more sympathetic to women’s issues. As Falstaff rightly pointed out, it is an error to continue to expect the same even when you learn more about that individual woman. But this error has nothing to do with the fallacy of division.