Let's look at the facts, I won't beat around the bush and share opinions with you, brother. Here is why women wear Hijab in Islam:
#1 Men have a much greater sexual desire than women, and they are aroused at the sight of women more so than women at the sight of men. I don't care what feminist thinks women and men are the same in getting aroused, it is just not the same for men and women. If women look at men, they do not have uncontrollable feelings, men get uncontrollable feelings when seeing women. Thus, women wear Hijab and are told to do so for this reason, which is just one out of many reasons.
#2 Modesty. The hijab is a form of modesty which has been around for ages. It is for class distinction. Rich and powerful families, and even women from other religions were told to wear the headscarf as a form of modesty. This is not a new phenomenon which Islam has created and enforced. This is a human phenomenon. Does anyone want their women stared at by men who have ill intentions, and do they want their sights on their women who they would protect with their life? It is not just Muslim men who are like this, men of all backgrounds feel greatly offended when the women of their family or liking are treated badly. This is why men fight over girlfriends and even just friends who are girls. They try to protect them from others. This is a form of prevention. Men do not gaze at women in any ill-manners in this way.
#3 The Hijab was introduced so that Muslim women do not get molested. The specific reason was because the wives of the Holy Prophet (saw) and the Muslim women would get treated badly like the slave girls did by being spoken to in a bad manner or being referred to in a humiliating way. So, in order to distinguish themselves, all the Muslim women were told to cover themselves so that they be distinguishable and thus respected for their status. The wives of the Holy Prophet (saw), and all the other Muslim women after them, were the best women of their time. They were to be treated differently and they were to command that respect by dressing a certain way.
#4 By raising the consciousness of women to cover themselves up, we prevent the sin which Western society is guilty of - objectifying women. Women who cover up are not kept hidden from society, but they are kept respectable in society. Women are supposed to be kept somewhat hidden so that everything is not known about them. If they wear something, it should not be the talk of everyone. Even among women themselves, they gossip and talk about useless matters with one another. This is a female trait in general. Men and women think differently about others, and the perception of women about other women isn't always so nice to each other. Therefore, a woman in public who is covered up isn't stared at by other men, and is not gossiped about needlessly by other women. Gossip spreads quickly. It isn't foreign to Western society either. I don't care what Atheists say about that. Women have also been objectified in this society by removing their coverings and clothing, and continuously shedding off any layers of clothing they can on billboards, TV, movies, etc. It seems their pride is in how often they can remove their pants. The honor of women in Western society is such that the more naked a woman is, the more honorable she becomes. While in Islamic society a woman who covers herself properly is honored. Who has more self-respect, the feminist who wants to experience hundred of male partners and goes naked whenever she can because she claims she is free? Or the woman who doesn't allow herself to be soiled by many men and dresses modestly in public?
I think I covered many more points within each point here for you. I will return with more points if I find there is more I can add to here. There are definitely some sources with good facts which can be used in an argument.
As for why men do not wear a Hijab, this is the other part of the question. But I think the reasons for why women wear Hijab should tie into that answer for you.
There is a situation in the West where people seem to feel uncomfortable with women who wear a Hijab, and wonder what they have hidden underneath (obviously of weapons or something else harmful) or because their face is covered. This is purely cynicism and racism combined, because the West groups all Muslims as terrorists and because they think all of us Muslims are up to no good. They have no argument to ban Hijab and no argument to speak against it considering their own hypocritical attitudes. If you look at some of the old black and white American movies, some women wore headscarves in public in the past. They may not have covered their faces, but aristocratic women and generally women of high class used to do so. They would be kept hidden in public.
