"Nearly a dozen" White House staffers have told Washington Post reporters that Trump was "demoralized" by press reports that showed a poor turnout for his inauguration and a much larger turnout for the Women's March the next day, and overruled his advisors and aides' advice to let it go — instead, he ordered press secretary Sean Spicer to tell a series of easily falsifiable lies to the media that misrepresented the turnout for the inauguration.
Spicer's poor performance at that press-conference — shouting words from a prepared, printed statement while wearing an "ill-fitting suit" and looking uncomfortable — further enraged Trump, and has highlighted the rift between Trump's family (notably, his son-in-law Jared Kushner), the staff that came with Trump from his campaign, and new hires like Spicer, with backstabbing and vicious whispers being the order of the first days of the Trump White House.
Ordering subordinates to lie is a well-understood political tactic. As Tyler Cowen writes on Bloomberg, it is a useful loyalty test and also a means of cementing underlings' dependence on dictators: by forcing spokespeople to tank their own credibility, autocrats ensure that their victims are totally dependent on them and their continued power for their livelihoods.
By requiring subordinates to speak untruths, a leader can undercut their independent standing, including their standing with the public, with the media and with other members of the administration. That makes those individuals grow more dependent on the leader and less likely to mount independent rebellions against the structure of command. Promoting such chains of lies is a classic tactic when a leader distrusts his subordinates and expects to continue to distrust them in the future.
Another reason for promoting lying is what economists sometimes call loyalty filters. If you want to ascertain if someone is truly loyal to you, ask them to do something outrageous or stupid. If they balk, then you know right away they aren't fully with you. That too is a sign of incipient mistrust within the ruling clique, and it is part of the same worldview that leads Trump to rely so heavily on family members.
Why Trump's Staff Is Lying
[Tyler Cowen/Bloomberg]
The first days inside Trump's White House: Fury, tumult and a reboot
[Ashley Parker, Philip Rucker and Matea Gold/Washington Post]