MENACHEM BEGIN had rejected any thought of a serious probe of the Beirut massacre, but a massive unraveling of his own government loomed, and a tenth of the country's population, Jews and Arabs together, took to the streets to protest. Mr. Begin came back from Yom Kippur, the traditional Jewish day for soul-searching, and accepted a full judicial inquiry into "all the facts and factors" relating to the massacre.

It could not have been easy for Mr. Begin to head down a road leading, possibly, to greater national embarrassment for Israel and political embarrassment for himself. But then it was no longer possible, if he wished to continue governing at all, not to head down that road.

Inevitably, the inquiry and the discussion surrounding it will make Israelis ask whether the conduct of their military in relation to the massacre was an isolated incident or the extension of broader policies and attitudes, especially in regard to the Palestinians. This could become the heart of the matter.

The Israelis, Mr. Reagan suggested on Tuesday, are "proving with their reaction to the massacre that there's no change in the spirit of Israel." He is right. The Israelis feel they must prove, first to themselves, that they are still true to their deepest impulse of compassion for people as innocent and defenseless as once -- many times -- they were themselves. They accept the moment as one for conscious self-definition, notwthstanding the likely costs. Is it too much to expect that the Lebanese, whose people actually consummated the terror at Shatila and Sabra, might also decide to fix and accept their share of the responsibility for it?

In Israel and elsewhere, attention focuses on whether Mr. Begin, or at least his defense minister, Ariel Sharon, can survive the process of inquiry. It will come as no surprise that we hope they will not. Mr. Begin, it has long seemed to us, ended -- nobly -- the period of his useful service to his country by the peace treaty with Egypt; the now-central Palestinian issue is beyond him. Mr. Sharon's high talents come wrapped in attitudes of personal and national arrogance increasingly widely seen to menace Israeli democracy and humanism.

The Israeli people, however, hardly appear to be in need of political kibitizing from their foreign friends. Indeed, such advice can backfire. Whatever the government with which Israel emerges from this ordeal, the United States will work with it, and urge it to make peace.