Not very convincing. According to this logic, everyone is a bisexual who wants to have sex with all of their friends, or either need to redefine 'man'/'woman' in this (all?) contexts. Unless assuming essentialism as related to sexuality, which has some problems, such as how to explain the fact that most people are neither entirely heterosexual or homosexual, for example (citation: Kinsey report).

By the way, I would argue that man/woman are more than sexual definitions. They are also social, moral in some religions, biological...