In seeking to restructure the nation's bilingual education aid, the Reagan administration yesterday reopened one of the most emotional, longest-running and politically explosive debates in American education.

Education Secretary William J. Bennett pronounced the existing "bilingual-only" federal policy a failure, responsible for a range of ills besetting Hispanics in education. The program teaches children in their native language until they learn English. He said he would act to give local school districts more "flexibility" in teaching children with limited English.

But Hispanic leaders and supporters of bilingual education responded quickly by pointing out the enormous educational gains Hispanics have made in the last two decades.

"Recent improvements in test scores -- particularly by Hispanic students -- are the results of federal programs started in the 1960s and 1970s, including bilingual education," said Rep. Augustus F. Hawkins (D-Calif.), chairman of the House Education and Labor Committee.

At issue in this debate are conflicting interpretations of the success of the existing program, as measured by test scores of Hispanic students on standardized exams, dropout rates, college attendance rates and reading ability. The measures can be read differently depending on what point is being made.

For example, critics of bilingual education -- including the Education Department officials who briefed reporters yesterday -- pointed out that Hispanics have a 40 percent high-school dropout rate. Supporters contended, however, that the dropout rate was at least 75 percent before the bilingual program was instituted.

Supporters of the current bilingual education program sharply criticized Bennett's initiative, accusing him of pursuing a "hidden agenda" to dismantle the program while playing the chords of an anti-Hispanic backlash that many see growing across the country. This backlash, they said, is manifested by groups such as U.S. English and by efforts to establish a constitutional amendment making English the official national language.

"Bennett is calling for the virtual eradication of the bilingual education program . . . ," Rep. Henry B. Gonzalez (D-Tex.) said. " His plan would deny the right of an equal education to millions of children."

"They're slowly walking away from the responsibility to teach limited-English children English," said John D. Trasvina, legislative attorney for the Mexican-American Legal Defense and Education Fund.

Trasvina mentioned the new national Scholastic Aptitude Test scores, released in New York this week, in which Mexican-American and Puerto Rican students registered the greatest improvement. "This is the type of progress that is going to be endangered," he said.

"Asking for 'flexibility' is saying, 'you guys handle it out in the hinterlands.' He says he wants to get politics out of it. He is putting education into the politics of many small towns in the Southwest, where Hispanics have historically faced electoral and other types of discrimination," Trasvina said.

Administration officials, anticipating the negative response from Hispanic leaders, pointed out what they called a possible schism over this issue between leaders of the Hispanic organizations, who are vociferously probilingual, and members of the Hispanic community, who may be less so.

"We are hard pressed to conclude that Hispanic parents do not want greater flexibility," Undersecretary of Education Gary Bauer said at a news briefing yesterday. "We do indeed believe there is something of a gap between the groups and the people they pretend to speak for."