My arguments was called "mansplaining", just because I'm a man and my opponent was a woman.
This is a classic "ad hominem" logical fallacy. If they truly have a good argument and think yours is not good, they should be able to defend theirs and attack yours without reference to the person arguing. If they need to resort to this kind of fallacy it demonstrates a weakness in their argument.
It's also ignorant sexism. The term 'mansplaining' refers to the tendency of an explanation needing to come from a man for social reasons, and highlights a particular common facet of sexism against women. Using it to justify ignoring an arguement because a man puts it forward is simply ignorant sexism on their part.
In terms of the burqua, there are two sides to the arguement. The first is that, by covering up their bodies, women can relate to eachother and to men in public without being seen as a sexual object. This can be very useful in avoiding some aspects of sexism.
The other side is, however, that western culture fairly consistently encourages people to express and celebrate all aspects of their identity, and sexuality is one such aspect. As such, there is nothing particularly wrong with expressing sexuality in public. And this is where the idea of Islam as protecting women from sexism really breaks down, because Muslim cultures are not just cultures in which burquas are an option, they are cultures in which it (or something like it) is compulsory. The very idea of public sexuality is prohibited, woman in particular, are effectively banned from expressing it. This leads to the twin ideologies of patriarchy (woman must be protected and cared for by men, and hence controlled by men), and the idea of chastity versus immodesty, in which any woman who does not protect their sexuality from everyone, has no right to protect it from anyone who wants to take it by force. Thus young woman really don't have to worry or concern themselves with their sexuality, which is what is being argued is so liberating, but only because others will be disposing of it on their behalf.
Thus you can argue that Muslim woman are free from social pressures of public sexuality, but this is only the case because their sexuality is not really seen as theirs to be responsible for. It's just a modern version of the old pro-slavery arguement that black people are better off being slaves, because as property they enjoy a fair amount of independence already and having more would simply be more responsibility than they could handle, and make them worse off.
The rest of this gets pretty speculative.
The idea I'm playing with on why this arguement survives at all comes down to the cultural differences between the West and the Middle East. In the West, freedom is good, and being under someone else's authority is bad. The emphasis is thus on freely choosing to follow someone else's leadership, typically by an appeal to higher principles that the leader espouses. In the Middle East, good is being under good and just authority. The emphasis is thus on choosing the correct authority to submit to, generally by an appeal to the higher principles that those who submit to that authority end up following. The principles are seen, not in the leader, but in his followers, and the independence and growth that they enjoy under his guidance. Thus in the West, the individual is vital, but in practice is expected to submit to an ideal. In the Middle East the submission to an ideal is vital, but in practice is expected to lead to the betterment of the individual. This may be why Western individuals are seen as encouraged to do really irresponsible things, while MiddleEastern leaders are seen as encouraged to do really irresponsible things.
There may also be a difference in how important things are dealt with. In the West we actively try and treat important things badly - sex is debased and described in the crudest possible terms, leaders are held up to public ridicule, and in general the more important something is the more we try and show it in a bad light. The reason we do this is precisely because we fear the tyranny of the sacred - that something will be held as so overwhelmingly important, that everything else must fall by the wayside. Our classic picture of a mindless fanatic is one who holds only one thing to be important. We balance this with tolerance - we are each going to hold different things to be important, so of course one thing can't be too important or else everyone will suffer.
In the Middle East important things are treated with great respect. Leaders are not lampooned, sex is protected, and religious is not routinely mocked. Such measures are only taken with things we want to remove, destroy or change, so any attempt to do that to something important is a threat. The counterbalance to this is of course far less tolerance. These things are important, so anything that threatens them is wrong and must be resisted, opposed or punished.
I'm floating a theory here - I've got no particular back up for this view, and I'm not sure how strongly I believe it, but it's my if-you-put-a-gun-to-my-head take on some of the biggest differences.
