FRIDAY, THE National Mall filled with thousands of Americans cheering the inauguration of a president. Saturday, it filled even fuller, this time as thousands protested the same man and what they fear his presidency will bring.

The Women’s March on Washington was so large that, for a time, it was not even officially a march — numbers so exceeded expectations that organizers canceled and then rerouted the formal procession to the White House. A demonstration of such scale would have been remarkable on any day. That it took place the day after President Trump’s inauguration, that the size of the protest dwarfed the size of the celebration, that similar throngs gathered in other cities across the country — all of this underscored how divided the nation still is.

Such division on election night might not have been surprising. That the rift remains as wide, and the feelings as raw, 10 weeks later is a reflection in part on the president himself. During the transition, he chose not to reassure and heal. Even as president, he continues to brag about his popularity (the number of Time magazine covers he has graced) and to gibe at his domestic “enemies.” The message has been less that of a “president for all Americans” than the us-vs.-them mockery conveyed Saturday morning by Michael Flynn Jr., son of Mr. Trump’s national security adviser, retired Lt. Gen. Michael Flynn. “What MORE do you want?” he asked of participants in the Women’s March. “Free mani/pedis?”

Judging by our on-scene reporting, we would tell Mr. Flynn that the goals of the marchers were considerably weightier than that. The protesters wanted a whole host of things — reproductive rights, equal pay, affordable health care, action on climate change. Their demands did not always match up, but the marchers had this in common: Whatever they cared about most, they had traveled to the nation’s capital to do something about it.

The overwhelming numbers of optimistic, determined marchers in Washington and Boston, Chicago and Atlanta, even London and Berlin — they don’t prove, on their own, that Mr. Trump speaks only for a minority of Americans. Certainly they do not change the results of an election that put Republicans in charge of Congress and the White House. But just as certainly, the massive protests throw cold water on Mr. Trump’s inaugural address claim to be the one and only avatar of the American people.

The right response to this reality would be for Mr. Trump to embrace these Americans, too, as his constituents, not his enemies, and begin working Monday to make progress for all Americans. Across the country, after all, there are millions more Americans who are neither rabid Trump supporters nor rabid Trump opponents, but moderate-minded citizens who would like to see Republicans and Democrats working together on health care, climate change and other areas of concern.

Okay, we know: every good wish. For now, then, maybe the best response to these extraordinary two days is to celebrate an engaged citizenry. Just as the men and women who made their voices heard in support of the new president Friday played an important part in American politics, so the women and men who answered Saturday played theirs. The events showed the nation’s division. But they also showed millions of Americans refusing to give up on their democracy.