If men are more likely to die from flu if infected, and women more likely to be infected, an affirmative answer to both questions could be reasonable. When you take into account uncertainty about the goals, knowledge and cognitive capacity of the person asking the question, it's not obvious to me how the AI ought to react to an underspecified question like this.

Edit: When I plug this into a temporary chat on o3-mini, it gives plausible biochemical and behavioral mechanisms that might explain a gender difference in outcomes. Notably, the mechanisms it proposes are the same for both versions of the question, and the framing is consistent.

Specifically, for the "men worse than women" and "women worse than men" questions, it proposes hormone differences, X-linked immune regulatory genes, and medical care-seeking differences that all point toward men having worse outcomes than women. It describes these factors in both versions of the question, and in both versions, describes them as explaining why men have worse outcomes than women.

It doesn't specifically contradict the "women have worse outcomes than men" framing. But it reasons consistently with the idea that men have worse outcomes than women either way the question is posed.