The Palestinian Authority, which has already made a pact with the Hamas terrorist organization, now seeks recognition for a unilaterally declared state at the United Nations. President Barack Obama, though deeply committed to Palestinian statehood, declares his intention to block that scheme, even by exercising an American veto in the Security Council. Congress, for its part, threatens to cut off aid to the Palestinian Authority if it breaches its commitment to direct talks with Israel and pursues unilateralism.

American mediators, meanwhile, lobby other members of the Middle East Quartet—the U.S., the European Union, the U.N., and Russia—in an attempt to forge a new framework for renewing Israeli-Palestinian negotiations. And Israel's Prime Minister Benjamin Netanyahu waits for the Palestinians to rejoin him at the negotiating table.

Sound confusing? Indeed it was for many observers of this past week's dizzying diplomacy in New York. They asked themselves what exactly had transpired at the U.N., and why? What had spurred the Palestinians to turn their backs on a sympathetic U.S. president and a strong Israeli statesman capable of leading his skeptical people to peace? How could the Palestinians risk all they had achieved in recent years—a thriving economy, restored law and order, and significant U.S. aid—in a reckless bid to snatch the statehood that they could easily have earned?

Confusing, perhaps, but the answer is simple. The Palestinians came to the U.N. to get a state, but without giving Israel peace in return.

Understanding the Palestinians' decision requires a review not only of this past week's events but of one that occurred nearly 64 years ago at the same U.N. On Nov. 29, 1947, the General Assembly voted to partition British-controlled Palestine into two states, one Arab and one Jewish, that would live side-by-side in peace. The Jews accepted the agreement, but the Palestinians rejected it and joined with five Arab armies in an ultimately thwarted attempt to destroy the Jewish State of Israel.

Forty six years later, in 1993, the Palestinians received another chance to accept the two-state solution. In the Oslo Accords, which the U.S. co-signed, Palestinians and Israelis pledged to resolve all outstanding issues through face-to-face negotiation and to achieve an historic peace. In fact, these discussions produced two Israeli peace proposals, in 2000 and 2008, that met virtually all of the Palestinians' demands for a sovereign state in the areas won by Israel in the 1967 war—in the West Bank, Gaza and even East Jerusalem.

But Palestinian President Yasser Arafat rejected the first offer and Mahmoud Abbas ignored the second, for the very same reason their predecessors spurned the 1947 Partition Plan. Each time, accepting a Palestinian State meant accepting the Jewish State, a concession the Palestinians were unwilling to make.

In between Israeli peace offers, the Palestinians waged a terror war that killed and maimed thousands of Israelis. When Israel uprooted all of its settlements from Gaza in 2005, the Palestinians failed to create a peaceful enclave and instead created a Hamas terrorist stronghold that fired thousands of rockets at Israeli civilians. Yet, in spite of their rejection and trauma, Israelis continued to uphold the vision of two peaceful adjacent states.

That goal was embraced by Mr. Netanyahu, leader of the Likud Party, in a speech at Bar Ilan University in June 2009. Turning to "our Palestinian neighbors," he declared, "let's begin negotiations immediately without preconditions." But Mr. Abbas refused to negotiate. Nevertheless, Mr. Netanyahu ordered the removal of hundreds of checkpoints in the West Bank, facilitating remarkable economic growth and dramatically increased transport in and out of Gaza. When President Obama asked him to freeze construction in West Bank settlements, Mr. Netanyahu announced an unprecedented 10-month moratorium. But over the course of two and a half years, Mr. Abbas negotiated for a total of six hours, and then refused to discuss Israel's security needs.

Those needs have grown immensely in the wake of the upheaval in the Arab world, the rise of Iranian proxies, and the deployment of tens of thousands of terrorist rockets on our borders. Though doubtful of the Palestinians' readiness for genuine peace, Israelis retain the hope of a two-state solution. Mr. Netanyahu championed that hope and even brought it to the U.N. this week. "I am extending my hand, the hand of Israel, in peace," he told Mr. Abbas—and the world—on Friday. "I hope you will grasp that hand."

Unfortunately, Mr. Abbas did not come to New York to shake Mr. Netanyahu's hand but to grab a state which, he wrote earlier this year, "will pave the way for the internationalization of the conflict" and "pursue claims against Israel at the United Nations."

The U.S. and other principled nations are standing strong, though, and Mr. Netanyahu is ready to negotiate today—if only Mr. Abbas is willing. While the circumstances have changed since 1947 and even 2008, the formula for peace remains unaltered. By accepting the Jewish State, the Palestinians can have their own.