Just to correct a factual misunderstanding. Muslim women do not cover their faces to show respect to men-not their fathers or their husbands. In Islam, women cover their hair (and some, their faces) do so to be modest. That is the religious reason.
The idea of it being out of respect for men is a carryover from the Christian teaching of headship as regards headcoverings. That is the CHRISTIAN take on it, not the Muslim background. Muslims generally don't follow Pauline thought.
A sadder reality is that many women do it out of cultural acceptance. Some have no understanding at all religiously of why they would cover. They do so because their moms, grandma's and aunties do. Or, in limited places, they are required by law to do so. It isn't about respecting the headship of men whatsover unless they simply want to please their traditional family (men and women). So some DO cover because they want to please their family even though they don't feel like their faith as a Muslim requires them to. It is easier to cover than to converse with all their loved ones about why they don't.
In the US, there are a LOT of women who you would never know are Muslim because they do not cover publicly. They may dress more modestly than other women (or not!), but again, it is their choice. Most of my friends do not cover even their hair.
In the states, none of my friends cover their face. When I lived overseas, the face coverers were usually from very traditional bedu families, or just very rich famiies or converts. My friends who were converts were doing so out of their own conviction as they were unmarried.