Surely the word 'man' just refers to the species, homo sapiens? Words such as 'human' and 'mankind' are derivatives that have no gender connotation and cover all species members. There are some interesting parallels with other mammalian species. For example 'lion' and 'tiger' refer to the species but also denote the male of the species with separate words, lioness and tigress, to indicate the female of the species. Therefore, the words 'man' and 'woman' have lots of precedents in our language. Yet animals such as the elephant and giraffe do not have derivative words for the females so why don't we just stop using the word 'woman', call everyone a man and then everyone is equal?!
I have yet to have the privilege of discussing this with a woke .....