It began with the fight. The black kid hit white Billy McKelvie and Billy swung back. When the teachers at Francis Scott Key Junior High in Montgomery County pulled the 7th graders apart, they didn't only blame the black kid for starting it--they took Billy to the office, too.

"They called his father," remembers Billy's mother, Kathy McKelvie, "and made him leave his office just because Billy defended himself. ... That principal had two sets of standards, one for blacks and one for whites. Billy's not able to fight back against a black but the black was able to attack him."

With that and talk of changes in school policies that would bring more academically troubled children from poor areas of Silver Spring to her neighborhood school, Kathy McKelvie decided she had had enough of the Montgomery County public schools. This year she put Billy and his sister, Mimi, in private schools.

"I'd rather pay than stay in public schools," she says with disgust.

She is not alone. In Montgomery County-- which has the Washington area's best public schools, according to test scores and the number of students they have sent to college in the past 10 years--private school enrollment leaped 10 percent from 1974 to 1979. And those numbers do not include families who send their children to private schools outside the county. Billy McKelvie, for one, switched to St. Anselm's Abbey, a private school in the District.

The steady drain of students from Montgomery County's public schools goes against the common argument that parents put their kids in private schools because the public schools are such awful academic institutions. In fact, a survey of Montgomery County private school parents found that academic quality was not among their top three reasons for leaving the public school system.

While a tuition tax credit drive may be an understandable reaction in the District--with its much- criticized public schools--the number of parents placing their children in private schools in the counties, where there are supposedly good public schools, indicates that similar campaigns there may not be far off. And if the local tuition tax credit drives fail, there is still President Reagan's campaign promise to seek tuition tax credits nationally. The way the wind is blowing, a lot of people seem eager to give up on public schools. Why?

Most parents, like Kathy McKelvie, are concerned more about their children than about the ideal of public schools or the numbers that show public schools are handling more children, more poor children and offering more courses than ever before. Despite those accomplishments, the schools are still failing to deliver what McKelvie and a growing number of parents want: the certainty that the schools will not be a negative influence, that their children will be drug-free, well-behaved scholars who can get into good colleges and train for good professions.

That is the dream for any child. "Private schools are a consumption commodity," says Arthur Wise, a senior social scientist at the Rand Corp. "Rather than the principal motivation being disenchantment with the public schools, it may be that instead of buying a Mercedes-Benz the parents decide to send their child to a private school."

If Wise is right, then no matter how much improvement the public schools make in their academic performance, it will not be enough to stop the shift to private schools. That will happen only when public schools do not have to let in ragged, tough kids with academic problems, or black children who may make for racial trouble in otherwise white schools, and when the schools do not keep students who smoke dope, get pregnant and fight.

In other words, public schools are in trouble unless they become private schools.

"I was one of those who believed the Montgomery County schools' reputation of being top- notch," says Pat Greer, principal of Hearst and Eaton elementary schools, public schools in the District. She lives in Montgomery County but sends her children to parochial school. "In the elementary schools that reputation is well-deserved, but in junior highs I found that there were things going on that I didn't want my kids to experience. There was a lot of pot smoking, the kids didn't have to go to classes and no one told them to. . . . The other problem I had was that I didn't think the schools were going to give them the kind of education that would allow the kids to get into the best colleges and compete. There was a lot of grade inflation, and the atmosphere didn't encourage a student who liked school, who liked to read, to study and to talk current events."

In the 1980 study of parents who were putting their children in private schools, 53 percent said poor school discipline was the main reason for doing so. Forty-four percent said religion/values was the reason, which meant, according to the study, that parents felt Montgomery County schools "underemphasize values instruction (or neglect it completely). . . ." A third reason was that classes were too large. Academic standards were ranked fourth.

"A private school," says Georgia Irvin, admissions director of Sidwell Friends School, where nearly half the students come from Montgomery County, "is not bogged down by bureaucracy. That is the biggest difference between them. We pick our teachers, we have the ability to be flexible with students. . . . Parents don't always know why they want a private school, but they know something is different here. They have more faith in us."

What the parents know is that they can pay and not be bothered with the crazy politics of a school board, with busing questions or with a bad principal. Even with fast tracks and slow tracks that segregate the good students from the bad ones, public schools still cannot get rid of the politics, the presence of bad kids and some bad teachers. They are part of being a public institution. Even a public school graduate can see that.