An educated and cultured gentleman with a long record of service to his country sat on a sofa in a comfortable living room and tried to explain the fierce Israeli pounding of the Palestinian guerrillas trapped in West Beirut.

You see, he said, you have to understand the Israeli psyche, the history of the Jews, the pogroms of Eastern Europe and the Holocaust and 30 years of unremitting tension and warfare with Israel's Arab neighbors. What all that has produced, he went on, is an attitude that is reflected perfectly in the policies of Prime Minister Menachem Begin.

"Get hit; hit back twice," said the man, a member of the opposition Labor Party and no admirer of Begin. He repeated the phrase several times, his face reddening as he did and his fist jabbing the air. "Get hit; hit back twice."

For weeks now, this is what the Israeli military has been doing to the Palestine Liberation Organization forces in West Beirut. Israeli charges of PLO cease-fire violations have been followed, sooner or later, by heavy retaliation that reached a high point with Sunday's air, land and sea bombardment.

This strategy is now a point of open disagreement between the United States and Israel, as President Reagan made clear to Israeli Foreign Minister Yitzhak Shamir in Washington Monday. While the United States urges military restraint to improve the "atmosphere" for the negotiations being conducted by special envoy Philip C. Habib, Israel continues to believe, an official said today, that "if we put some additional pressure on the PLO this will help Mr. Habib succeed."

But there appears to be more to the adoption of this strategy than an instinctive desire to "hit back twice" and a calculation that only this will move the guerrillas out of West Beirut. Beneath all the bluster by Begin and others that Israeli patience is wearing thin, Israel also appears to have been trying to buy time in the hope of avoiding a decision it may not be able to put off much longer.

"The only thing that can really hurt Begin," the man in the Jerusalem apartment said, "is casualties."

Casualties have always had a special impact in Israel. With a population of only 3.5 million confined to a small tract of land hugging the eastern Mediterranean, every death on the battlefield seems more a personal loss than a cold statistic.

No one knows what the cost in Israeli dead and wounded would be in an all-out assault on West Beirut, but it is widely assumed that it would be high. The Palestinian fighters have had weeks to fortify their positions in the city and the Israeli Army is not accustomed to warfare in a heavily urbanized setting, which would tend to blunt its huge firepower advantage.

This war, the longest Israel has fought excepting the 1948-49 war of independence, so far has been one of the least costly in terms of its casualties. As of early this week, according to military officials, Israeli casualties since the invasion of Lebanon on June 6 were 295 dead and about 1,800 wounded.

Israel's losses in the lightning Six-Day War of 1967 were 777 dead and 2,811 wounded, and in the 1973 war, 2,527 dead and 5,500 wounded, according to military officials.

The Begin government appears reluctant to turn a long war into an extremely costly one as well. It has sought to put the PLO under the maximum military pressure with a minimum risk to its own forces .

But this strategy of long-range bombardment has had a political cost to Israel. The Jerusalem Post, quoting Lebanese police, said today that up to 238 people were killed as a result of Sunday's bombardment. If that toll is anywhere near accurate, it would approach Israel's total losses for the entire war.

Such casualty statistics--even when hotly contested by Israeli officials--have increased the condemnation of Israel and strained its relations with its most important ally, the United States.

Having decided in the early days of the war to go beyond its initial announced goal of clearing the PLO guerrillas from a 25-mile-deep corridor along Israel's northern border with Lebanon, the Begin government is now faced with the consequences of that decision and a dwindling number of options if the Habib mission fails.

Vows by Begin, Defense Minister Ariel Sharon and others to drive the PLO out of Lebanon appear to leave little room to back down. The casualties their troops have suffered since taking up positions around Beirut have caused no great outcry yet, but in a country that has vowed never again to endure a war of attrition, such patience will not go on forever.