It’s easy to see why political polarization is so bitter today in both Israel and America these days: Moderation is a “lose-lose” proposition, winning politicians no credit from their opponents while alienating elements of their own base. This problem exists on both sides of the aisle. But two unusually candid left-wing assessments of Israeli Prime Minister Benjamin Netanyahu provide a particularly clear example of how it works and why it’s bad for both sides.

In an interview with Haaretz last month, senior opposition politician Tzipi Livni noted (as I have repeatedly) that Netanyahu built very little in the settlements during his 10 years in office. “Why hasn’t Netanyahu built up until now? Because he gets it,” she said, referring to the Palestinian issue.

Moreover, she continued, “Bibi will not go out and start a war. In that respect, he is responsible.”

His problem, she charged, is that he’s under pressure from his rightist base on various issues, and sometimes, “he caves in to them. I’ll say it again, it isn’t him. I’ve spent hundreds of hours with him [as justice minister in the previous Netanyahu government, in which she was responsible for diplomatic negotiations]—his actual positions are different.”

What makes this astounding is that Livni and her compatriots on the left have spent most of the past decade saying exactly the opposite—that Netanyahu is responsible for massive settlement construction, that he’s anti-peace. And this has serious real-world consequences.

The first and worst is that this narrative, which Livni now admits is false, has been widely embraced by American Jews and the Democratic Party. That’s bad for Israel as a whole, as it has contributed to growing anti-Israel sentiment among both groups.

To be clear, I don’t think either group’s alienation stems primarily from Israel’s policies, whether real or alleged. Nevertheless, had prominent Israeli leftists told the truth—that Netanyahu was doing very little settlement building, that his “actual positions” are far from his hardline image—it might have slowed the process.

Second, this false narrative hurts leftists themselves since it impedes Netanyahu’s ability to adopt policies they favor. Many such policies, like the dearth of settlement construction, are indeed very unpopular with his base, but he could justify them if they were achieving something important for Israel, like maintaining its bipartisan support in America.

In reality, however, they don’t achieve anything. For instance, despite his restraint on settlements, the Obama administration repeatedly accused him of “aggressive” settlement construction, with full-throated backing from Israeli leftists. That makes it impossible for Netanyahu to justify restraint to his unhappy base, which is precisely why he sometimes “caves in to them.”

Finally, this false narrative hinders his ability to form a broader-based government. Far from being the “right-wing extremist” leftists term him, Netanyahu is a center-rightist, and he desperately wanted the Labor Party in his current government to balance the right-wing parties. But after months of negotiations with former Labor Chairman Isaac Herzog, it became clear that Herzog had no support for such a move within his own party. So Netanyahu ultimately brought in the right-wing Yisrael Beiteinu instead.

Nor is this surprising. Having told its own voters for years that Netanyahu was anti-democratic and anti-peace, Labor would have trouble persuading them that joining the government was justified. But had it instead told the truth about issues like Netanyahu’s settlement restraint and diplomatic moderation, joining the government (and thereby pulling it further to the left) might have been an option.

Two days after Livni’s interview ran, Jerusalem Post columnist Susan Hattis Rolef, who has worked for various senior Labor politicians, published a column lamenting that “in the past Netanyahu could be trusted to block legislative proposals that were blatantly undemocratic,” but today, he “no longer seems to bother himself with acting as a barrier against threats to democracy coming from the direction of his own coalition.”

Here, too, what’s shocking is that Rolef and her compatriots on the left have spent the last decade saying exactly the opposite. Netanyahu has indeed allowed legislation in his current term that he would previously have quashed (most of which isn’t actually undemocratic, but that’s a separate argument). Nevertheless, the claim that he’s responsible for “anti-democratic” legislation didn’t just arise this term; prominent leftists have accused him of that for the last 10 years, even though, as Rolef now admits, he spent most of those years blocking proposals the left considered “anti-democratic.”

Again, the damage is threefold. First and worst, the false narrative that Israel is becoming increasingly undemocratic has contributed to growing anti-Israel sentiment among American Jews and the Democratic Party.

Second, it hurts leftists themselves, by reducing Netanyahu’s ability to adopt policies they would prefer. It’s hard for him to justify killing legislation his base supports unless doing so achieves something useful for the country. But in fact, his years of quashing bills the left disliked accomplished nothing since Israeli leftists still accused his government of being anti-democratic, and American Jews and non-Jewish leftists believed them.

Finally, this false narrative impedes his ability to form a broader-based government. Had Labor joined the government, it would have been able to kill any legislation it considered undemocratic, as coalition agreements usually give every party veto power over issues particularly important to it. But after falsely telling its voters for years that Netanyahu himself was anti-democratic, how could it justify doing so?

Many of the same evils obviously derive from Israeli rightists’ favorite trick of calling left-wing opponents “anti-Zionist,” though most Israeli leftists are no such thing. Inter alia, the false narrative that anti-Zionism is widespread on the Israeli left helps legitimatize anti-Zionism as a normative left-wing position overseas.

But since Netanyahu has led Israel for the last decade, the greatest damage has come from the left’s false narratives about his beliefs and conduct. And in the end, everyone has lost by it. Netanyahu, and by extension the entire center-right, has been unjustly tarred as anti-democratic and anti-peace. The left has forfeited its ability to block policies it opposes and promote those it supports. And Israel as a whole has seen its image overseas undeservedly tarnished.

Evelyn Gordon is a journalist and commentator living in Israel.