Elon Musk insists he isn’t an antisemite.

But this past week, the billionaire entrepreneur left many wondering. At the very least, a string of inflammatory tweets he sent Wednesday showed how gratuitous Musk can be and how easily tweets on his own social-media platform can be misleading and trigger him.

His tweets called an antisemitic post “the actual truth” and renewed his pointed criticisms against the Anti-Defamation League, a Jewish advocacy group that he has described as pushing a “woke mind virus” hurting free speech and, in turn, his business, Twitter-turned-X.

It was an unexpected provocation six weeks after Musk and the ADL appeared to reach a detente after an earlier escalation. And once again his self-generated drama is hindering his pursuits.

He has drawn a tidal wave of negative attention at the moment when he was supposed to be a shining example of American excellence at the Asia-Pacific Economic Cooperation conference in San Francisco and overseeing the potentially historic launch of SpaceX’s large rocket scheduled for Saturday.

Instead, Drudge Report was running a banner headline naming him the “world’s richest bigot.” Longtime vocal Tesla investors were expressing dismay in their famous CEO. Apple, Disney and other major advertisers suspended spending on X, opening a serious new risk for the company. And the White House was condemning Musk’s “abhorrent promotion of antisemitic and racist hate in the strongest terms, which runs against our core values as Americans.”

A close study of his tweets Wednesday helps show what prompted him to go nuclear against the ADL. His ugly detour began shortly after the lunch hour in California when Musk came across a tweet from the kind of user he might consider one of the so-called citizen journalists he has become obsessed with on the platform.

“Fake corporate new media is making up stuff again,” began a post by an account called Wall Street Silver, run by Jim Lewis and Ivan Bayoukhi and followed by more than one million users, including Musk.

Wall Street Silver, which has its roots in a Reddit forum dealing with metals, included a screenshot of an MSNBC broadcast about the rise of hate speech at Twitter under Musk that cited data from the ADL. “Not exactly legitimate objective sources,” it concluded.

Musk responded. “They really should just drop the ‘A’ and go with Defamation League,” he wrote. “Way more accurate.”

In the roughly two hours that followed, the billionaire’s rhetoric grew hotter as he continued to name check the ADL. One could almost see anger building in real time as what Musk’s biographer has dubbed his Demon Mode exploded online for all to see.

At one point, Musk tweeted support for a random X user’s post espousing the same sort of vile conspiracy theory about Jews replacing whites that was spewed by a killer who shot up a Pittsburgh synagogue in 2018. That reply by Musk—“You have said the actual truth”—ignited the firestorm against him.

He kept going.

“The ADL unjustly attacks the majority of the West, despite the majority of the West supporting the Jewish people and Israel,” Musk tweeted. “This is because they cannot, by their own tenets, criticize the minority groups who are their primary threat. It is not right and needs to stop.”

When a user pushed back that it wasn’t fair to generalize against the Jewish community at large, Musk mostly agreed: “You right that this does not extend to all Jewish communities, but it is also not just limited to ADL.”

He added, “And, at the risk of being repetitive, I am deeply offended by ADL’s messaging and any other groups who push de facto anti-white racism or anti-Asian racism or racism of any kind. I’m sick of it. Stop now.”

What makes the whole episode even more of an unforced error is that the MSNBC screenshot was from almost a year ago, though the Wall Street Silver tweet doesn’t mention that. Lewis and Bayoukhi each responded to requests for comment with a giant poop emoji.

Wall Street Silver’s X account is the kind of user Musk has been interacting with more and more as he works to promote so-called citizen journalists, or content creators, that he’s betting can create the types of viral posts that make X the place to be for a whole host of topics.

This month, Musk has averaged a daily reply on X to Wall Street Silver, which often covers a wide array of current events through a sensational or conservative lens.

Under X’s new revenue share program, certain paying users, such as Wall Street Silver, have new motivations to see their tweets go viral as more engagement can generate larger payouts.

Wednesday’s Wall Street Silver post about the ADL was viewed more than 1 million times through Friday, according to X’s count.

Musk’s citizen journalism effort has been tested since the outbreak of the Israel-Hamas war in October and the subsequent flood of posts involving the conflict—some filled with very real images and others not so much, including old video clips misleadingly repurposed.

The company’s ability to handle hate speech and misinformation has been under heightened scrutiny, including from the ADL, since Musk acquired Twitter in late October 2022. The ADL’s research, suggesting a spike in antisemitism, helped fuel news stories that fall, including that MSNBC story.

“Today, we are joining dozens of other groups to ask advertisers to pause Twitter spending because we are profoundly concerned about antisemitism and hate on the platform,” the ADL tweeted shortly after Musk took over.

In the weeks that followed, Musk dismantled much of the company’s infrastructure around content moderation, moves that left some advertisers and others worried X would be left more vulnerable to offensive content than rivals.

The changes were partly framed by Musk as being made to combat an overly liberal mindset that squashed free speech on the platform, especially among more conservative voices.

In September, Musk lashed out at the ADL over its criticism, blaming his company’s advertising woes on pressure the group applied to brands—claims it denied.

To Musk, the ADL was a progressive liberal group looking to silence speech and part of the “woke mind virus” he had vowed to push back against.

“Since the acquisition, The @ADL has been trying to kill this platform by falsely accusing it & me of being anti-Semitic,” Musk tweeted.

Musk’s aggressive rebuttals, including threatening to sue the ADL, came as his newly hired X Chief Executive Linda Yaccarino had been trying to smooth things over with advertisers and the ADL.

By Oct. 4, a detente was reached between Musk and the ADL. The group issued a statement announcing it would resume advertising on the platform. “We appreciate @X’s stated intent over the last few weeks to address antisemitism and hate on the platform,” the ADL tweeted.

Musk thanked the group in his own tweets. Then came Wednesday.

Write to Tim Higgins at tim.higgins@wsj.com