Research from Harvard University's Alison Wood Brooks says that failing to share how we've failed (and talking up our accomplishments too much) triggers "malicious envy" in peers. Such envy creates dysfunctional behavior as peers, or even direct reports, seek to tear down and undermine the successful leader, even while considering unethical means to do so as justified. It also leads employees to behave less cooperatively and disrupts a sense of teamwork.
Brooks's research makes this clear. In one study, participants read a paragraph about the successes of a leader and reported feeling a high amount of malicious envy toward that leader. Another group read the same paragraph, but this time the paragraph included a few extra lines at the end describing the leader's setbacks and failures, as well. That group reported feeling no envy.
Interestingly, the research also showed that measured admiration for leaders doesn't decline when they learn of a leader's failures. In fact, when employees hear a leader talking about their mistakes, it can induce "benign envy" where the employee feels that the leader deserves their success, and, in turn, they feel inspired to improve their own performance.