I've heard horrible stories from the Muslim world about how women can not get needed medical care because their husbands refuse to let them see a male doctor (these women definitely don't get gynecological care, breast exams, or pap smears, because their husbands won't let them go to a male doctor for these things). Female doctors in the Muslim world are almost unheard of, although some exist. So if women have a medical problem that needs to be treated they often have to suffer in pain in silence.
Imagine having a cavity and having it cause you pain day after day, with no way to get help because there are no female dentists. Imagine the tooth rotting and being unable to eat on that side, and waking up every day to pain until the tooth just rotted and died.
In a medical situation it may be impossible to know whether the needed medical treatment is something minor or something that may save a life. An itchy mole could be benign or cancerous, for example.
And what's wrong, in a business situation, such as two CEOs meeting, with them shaking hands? Are they going to jump on each other in the boardroom in front of other workers in a business meeting?
Doing things like this would restrict women's power in the business world.