Respect of women and their rights to their own body and whether or not they allow men to touch them is at the very core of this answer. Keep in mind, Allah is the one who knows best what he has created and what the needs and limits are for each of us. Shaking hands (and touching) members of the opposite sex when [not] closely related, is not permissable for Muslims according to the teachings of Islam.Muhammad hated women (scroll down a bit here), which is why he preached and practiced polygyny, child sex slavery ('Aisha, the Mother of the Believers. And don't try to lie: she was only a poor, prepubescent nine-year-old when he started raping her as his favorite "wife"), sex slavery, rape, murder, wife-beating, and oppressive, discriminatory laws making women (and little girls) into chattel.
And don't try to justify his murderous misogyny by claiming it was done out of "respect" or "Allah knows best."
There's no one on Earth who doesn't know that Muhammad's laws regarding women are wrong for him.