Genesis was originally written in Hebrew, and the early chapters of Genesis use two different Hebrew words for man: adam and ish.
Adam can mean either man, human or humankind, or it can refer to the specific person named “Adam”. Translators have to determine the meaning from context. For example, in Gen 2:20 the word is translated “the man” the first time it occurs and “Adam” the second time it occurs. In Gen 5:1-2, the word applies to both Adam and Eve. In older Bibles it tends to get translated “man” most of the time, as the English word “man” used to have the same ambiguity. In newer Bible versions (e.g., TNIV and NRSV), the translators have tended to use “human” or “humankind” whenever the word appears to refer to females as well.
Ish is more specific and means male person. It is used in Genesis 2:23:
Then the man said,
“This at last is bone of my bones
and flesh of my flesh;
she shall be called Woman (ishshah),
because she was taken out of Man (ish).”
So the translators do not have to guess from the context when ish is used. It is unambiguous.
This usage comes into the New Testament sometimes as well. James, who writes in a very Hebrew-influenced Greek and uses “aner” (man) where Paul would use “anthropos” (human), unless quoting the Greek Old Testament where usage like James’ is common.