A VERY UNFORTUNATE proposal," said the headmaster of the National Cathedral School. "What it would do to the public schools is just destroy them," said the business manager of St. Albans School. "We're in favor of a good public school system and a sound city." They were talking, of course, about the misguided attempt to establish a city tax credit for school tuition. It will be on Washington voters' ballots on Nov. 3.

The widespread opposition among the private schools springs from the enlightened view that the debasement of public education can bring only harm to private education. The idea is to let families deduct school tuition, up to $1,200 a child, from their city taxes. Parents who find that idea appealing need to consider the arithmetic more carefully. That $1,200 per child is enough to do real damage to the city's tax base and its public school system. It's not enough to establish and run new private schools of quality.

In an attempt to meet that obvious objection, the sponsors of the initiative have added a provision offering businesses credit of up to half of their city taxes for donations to private schools. If the voters give away half of the commercial tax base, what's going to pay for city services--not only the schools, but health, police protection and all the rest? The Greater Washington Board of Trade joined last week with the Greater Washington Council of Churches, the Washington Urban League and the National Council of Christians and Jews in urging voters to reject this unwise and deeply harmful idea.

Earlier, Archbishop James A. Hickey announced that he would not try to influence Catholic parents one way or the other. He noted that most of the city's Catholic pupils were in the public schools, and that he is concerned for all children in all schools.

Who's left in favor of this thing? Go down the list of the putative beneficiaries. If the business community is against it, if the private schools are either opposed or neutral and if the archbishop refuses to support it, who's for it? Who, other than zealots and idealogues hostile to the principle of public education and the opportunity that it offers to every child, regardless of his parents' tax status?