The custom of covering the head signifies one who is in subjection. This is contrary to what a man ought to be as Matthew Poole puts it well, “to uphold the power, pre-eminence, and authority with which God hath invested him.”
God made man to own the headship of His creation – Genesis 1:26-28 And God said, Let us make man in our image, after our likeness: and let them have dominion over the fish of the sea, and over the fowl of the air, and over the cattle, and over all the earth, and over every creeping thing that creepeth upon the earth. So God created man in his own image, in the image of God created he him; male and female created he them. And God blessed them, and God said unto them, Be fruitful, and multiply, and replenish the earth, and subdue it: and have dominion over the fish of the sea, and over the fowl of the air, and over every living thing that moveth upon the earth.