TL;DR follows

I was in a conversation with a feminist coworker and she brought up the pay gap, and we quickly got on the tangent that if more women would step up into rougher jobs, that earnings gap would diminish. Men are 90% or better in sanitation, mining, oil, etc. all of which pay quite well. She went on about equity is the goal, and women aren't allowed to go into those fields, or are disuaded from them. I brought up how that the more equal a society, the sharper the division in male/female labour. That women CHOOSE not to go into thise careers.

So I asked, if those jobs pay well, but women refuse to do them, how can we have equity? Of course her suggestion was to just pay women more, but when I pointed out that there are severe civil rights violations to make business X pay only the women more because a guy in business Y makes more than they do. She agreed that was silly, then it hit me. An epiphany.

I asked her, "well, if equity is going to solve all the problems, then there is one sure fire way to get 50/50 parity in those fields: draft them. Naturally, she was incredulous, but I quickly reminded her that the draft is a real thing, and we do it for the military in time of war, why not an equity draft? As far as civil liberties go, the same arguments work for both, right? And it'll get us parity in the work force.

So, as an exercise in absurdity, what would be good arguments for or against it?

TL;DR I suggested using the draft to achieve equity in jobs women don't choose.