What other evidence is there for claiming Homer might be a woman?
I think a lot of the thinking for it is the very contrasting themes of the two books.
I always thought that was a tenuous argument. It always seemed more likely to me that a young Homer would want to write about glory and war, but once we get older, we tend to become more reflective. A homecoming to family seems like an appropriate topic for an older Homer.
Some experts think the contrasting themes too diverse to be consistent in the mind of one individual. Others think it quite appropriate for the younger Homer to be preoccupied with the blood, guts, and wrath of warfare, whilst the older, more reflective poet would find the topic of a homecoming to wife and child the perfect topic to write on in his golden years.