Why do Muslim Men have beards and Muslim Women have wear head and face coverings
Beards of the Muslim men:
Did Abraham, Moses, King David and Jesus, peace be upon them, have a beard or not? Do observant faithful male followers of Judaism have breads or not? The beard is the natural God given sign of manhood, and the universal distinguishing mark of masculinity from femininity. This is why all prophets of God like Noah, Abraham, Moses, Jesus and Muhammad, may Allah’s peace be upon them all, had beards and ordered their followers to keep their beards.
Muslims seek to maintain the way of the prophets in this aspect of the God given appearance of masculinity. Its as simple as that.
There are specific commands of the Prophet Muhammad, may the salutations of peace and blessings be upon him and his family and followers, that order the believers to maintain their beards and to trim their mustaches, and these commands are reported in authentic narrations in various phrases that make the command one of religious obligation not voluntary choice.
The head coverings, scarves and veils on the Muslim women
The virtues of modesty and chastity are the main reasons for Muslim women to wear head coverings, scarves and veil. Another reason is for protection from the disturbing teasing, ogling, and advances which may lead to molestation and lewdness forwarded by those unscrupulous and criminal elements in society. Islam seeks to protect the family life of the society in general, and thus seeks to protect the chastity and moral purity of all members of the society from temptations. This is the main rational for women to wear modest clothing.