In 1 Corinthians 11:7, Paul says “A man ought not to cover his head, since he is the image and glory of God; but woman is the glory of man.”
A man is to be in the likeness of God, but a woman/wife is the likeness of her husband.
1 Corinthians 11:16 – If anyone wants to be contentious about this, we have no other practice—nor do the churches of God.
The Jewish people have no other custom, and neither did the other Christian churches.
In Judaism, Jewish men cover their heads when praying, or attending a synagogue or religious event/festival. Wearing a skull cap is seen as a sign of devoutness.
However, there is no such commandment in the Bible for men to cover their heads. The idea of men covering their heads, comes from traditional sources outside of the Bible such as the Halaka: a collection of Jewish religious laws derived from the written and oral Torah. It also stems from the Talmud; a collection of different Rabbi’s interpretations of the Torah. Rambam, a very influential Jewish scholar who recorded his own interpretation of the Old Testament scriptures, also supported male head covering.
These are some of the sources outside of the Old Testament that created the tradition of Jewish men covering their heads. This tradition comes from various Rabbis and not from any Old Testament prophets or scriptures.
Many Jews feel that by wearing a skullcap, they are proudly announcing to the world that they are Jewish. This is classed as an outward sign of their faith.
Other Jewish sources suggest that the reason for the male head covering was to distinguish Jews from their non-Jewish counterparts, especially while at prayer.