The first issue is that Trump's overt record of misogyny, including a pretty clear case of sexual assault on his wife and a number of respectable accusers with perfectly plausible stories, means that there will be a groper and a chauvinist in the White House. It demonstrates that a substantial portion of the electorate simply does not care that someone with that degree of a breach of ethics will be representing our country to the world. I had people seriously try to explain that Hillary Clinton's normal actions within a complex system where she was far from the decisive voice that led to deaths outweigh Trump's personal tendency for sexual assault. Trump is therefore a litmus test for the populace. It shows that traditional, patriarchal, misogynist ideas are pretty deep in the body politic, such that enough people don't care about someone committing a felony. (So much for "rape culture" being a myth). Jordan Klepper's interview with Trump fans, including women, is eye-opening: We hear people joking about sexual assault (wanting him to grab terrorists "by the pussy") and normalizing it ("locker room talk", one man admitting he'd act that way if he had that kind of wealth and power), But the most disheartening folks are those who admit when pressed that neither they nor anyone they know would talk that way, and indeed they would be disappointed in the extreme if their children talked that way, but it's somehow okay when Trump does it.
Therefore, the marches are intended to indicate to the rest of the country that, no, this is not normal, this is not acceptable, and it can't be allowed to become either. It's an attempt to signal to those who are hardcore misogynists that they won't be able to barrel over women with the Gropenfuhrer in power, and an attempt to signal to those who are not, who admitted that the "locker room talk" response was an excuse, that they should not be silent or accept this.
Secondly, Trump ran as a far-right Republican. Noteworthily, Trump's stance on women's rights is actually fairly mixed, as a result of his transition from libertine playboy to fascist wannabe. Still, he's aligned himself today with the party that implements TRAP laws under fraudulent pretenses to deny access to the right of abortion, won't protect rape victims even when it comes to simply processing their rape kits in a timely fashion, and so forth. In the campaign, Trump flip-flopped on abortion constantly, but one of his positions was that women who seek out an abortion should be punished. That was so far to the extreme of the (admittedly-very-political-and-polished) present abortion consensus, which mostly seeks to punish the doctor, that it drew fire even from other Republicans.
We are looking, therefore, at a cabinet that is not just full of corporate stooges and corrupt plutocrats but also a cabinet that simply does not care one whit about women's issues.
One of the pieces of red meat that Trump can toss his base to keep his relatively-maverick policy-making is to fulfill his promise to get someone more extreme than Scalia through. Planned Parenthood funding will be cut, which of course does very little to actually reduce abortions but does prevent the poor from getting ultrasounds, mammograms, birth control and STD treatment. This matches full well with the Republican agenda to make sex out of wedlock so unpleasant as to deter anything besides their specific interpretation of sexual morality. The Hyde Amendment, which "bans certain uses of federal funds to pay for abortion coverage in a variety of health care programs run by the federal government, from those who access health care through government insurance programs or directly by using Medicaid or veterans’ healthcare, among others", is also likely to become entrenched and permanent.
Nor will the Trump administration be likely to do any kind of work to push efforts to deal with discrimination, improve the promotion of women in STEM fields or blue collar fields, protect female unionization, close the wage gap, break the glass ceiling, make forthright efforts to actually prosecute rape, or deal with anything else of note.
The best that can be said for the Trump administration's stance on women is that his hardline stance on Islam and his militarism might, in theory, benefit some women somewhere. In practice, though, American bombs have pretty rarely led to women's conditions improving in the Muslim world or anywhere else.
As a result of all this, I support the March as an initiative. In particular, as I've stated on Facebook, the March is not only a great example of peaceful protest covered pretty well by the media but is also an example of how much further we've come on the Left since 2000. While this may feel like a very scary time for progressives, the fact is that we have an immense number of recent movements, from Occupy to Sanders '16 to "Rape Is Rape" onward, under our belts, in ways that just weren't the case in 2000. There's real critical consciousness and real opportunities to civilize the culture. I prefer to view Trump as the last stand of the disease infecting the body politic, and this as the final feverish throes before we're able to achieve a real commitment to justice.