Why does Biblehub translate κεφαλῆς in I Corinthians 11:4 as "[his] head" the morphology states N-GFS? Why not "[her] head"?
Grammatical gender (in this case feminine) is not (usually) related to human gender. Most words have a single gender that is used in all sentences regardless of whether it belongs to a man or woman.
The possessive pronoun in the English of I Corinthians 11:4 does not come from the word for head itself, but rather is "added" to make the English grammatical. (Which is indicated by the brackets on Biblehub.) The Greek says simply "having on head" but that doesn't make any sense in English, so it becomes "having [anything] on [his] head."
As to why it is "his" instead of "her", in English the possessive corresponds to human gender. The subject of the sentence in I Corinthians 11:4 is "every man," so the corresponding possessive pronoun must be masculine. Think of it this way - if "head" was say "hands" you wouldn't be asking why it says "his" (singular) instead of "their" (plural). Grammatical gender works the same way.