There is actually a large debate in the Christian community on what that meant when written.
The Greek say man is the kephale, literally meaning the body part above the neck, of the woman. Head is a metaphor for leader in English, and reading our metaphor into it may not be what the metaphor meant in 1st century Greek.
Some Greek scholars favor “man is the source” as meaning, others “man is the prominent part”. Others believe it refers to the image of the man and women being a one-flesh union, with the head and body needing each other. Some favor leader, but it is not the only and obvious meaning as an English reader may suppose.
(The other interpretations are not new and inspired by the feminist movement either. For example, Greek speaking bishops of the 4th and 5th centuries wrote that head mean source in the two Bible verses that call man the head of women, and they were close to the language and idioms the Bible was written in.)