Share of homelessness due to an abusive relationship + share of homelessness due to drugs + share of homelessness for all other reasons = 1.
If one of those variables goes higher, one or both of the others must go lower. On the assumption that one of those reasons gets more common "all else equal"... both of the others will go lower.
In fact if you read what they wrote, they didn't specify sex at all. A man can be homeless due to an abusive relationship, they never said they couldn't. Hence independent statements. nsnick was the one assuming something.
A singular case subject/family could be homeless for MULTIPLE reasons or None (other than other of course) outlined above.
This is wrong. What's correct as a description of the entire female homeless population is equally correct as a probability assignment for one element of it.
Your second sentence is unrelated to your first, and also applies equally well to the entire population as to an individual sample from it. It is arguing that the sum I describe is in fact more than 1. That is defensible, but it won't make the statements independent; they aren't.
No, because someone can be homeless for multiple reasons.