These and other questions are carefully considered in "The Head Coverings of 1 Corinthians 11." Of great value is the material showing what the head covering customs were at Corinth. Rome and in first century society in general. You may be startled to find that Roman men were required to cover their heads when worshiping idols. You may be interested in the evidence of statues and paintings.
These and other things in this book will keep the Christian very interested. Thoughtful, reasonable, scriptural—this is how you will find this book. Whether you agree with the conclusions or not, you will find your thinking changed. This book will be a help to you.