This is literally a conversation about the meaning of a word.
Sexual reproduction requires both male and female haploid gametes. In most species, these gametes are produced by individuals that are either male or female. Species that have male and female members are called dioecious (from the Greek for 'two houses'). In some species, a single individual may possess both female and male reproductive systems. Such species are called monoecious ("one house") or hermaphroditic."
William K. Purves, David E. Sadava, Gordon H. Orians, H. Craig Heller (2000). Life: The Science of Biology. Macmillan. p. 736. ISBN 978-0-7167-3873-2.
https://books.google.com/books?id=kS-h84pMJw4C&pg=PA736
Definition of man (Entry 1 of 4)1a(1): an individual human, especially : an adult male human
https://www.merriam-webster.com/dictionary/man
Definition of woman. 1a: an adult female person
https://www.merriam-webster.com/dictionary/woman
male [māl]
an individual of the sex that produces spermatozoa.
Spermatozoa are not a social construct.
female [fe´māl]
an individual of the sex that produces ova or bears young.
Ova are not a social construct.