Arlington County Board candidates Stephen H. Detwiler and Mary Margaret Whipple faced each other in debate last week over tax rates and the firing of County Manager W. Vernon Ford.

Detwiler, the Republican incumbent, and Whipple, the Democratic challenger, held their first campaign debate before the Arlington Optimist Club, which met at the Washington Golf and Country Club.

Whipple, who ran unsuccessfully for the County Board in 1979, stressed that the board's majority is at stake in November's election.

"What the voters are going to be deciding is whether they want to continue the Republican majority of Walter Frankland, Dorothy Grotos and Detwiler, or whether they will build on the victories of John Milliken in 1980 and Ellen Bozman in 1981 and form a new majority, a Democratic majority, with the election of Mary Margaret Whipple," she said.

Republicans have controlled the five-member board since the election of Detwiler, now board chairman, in 1978. Detwiler is seeking a second four-year term as a Republican-endorsed independent.

Detwiler, in his talk, emphasized the reductions in the county's real estate, personal property and business license tax rates since his election to the board. During the debate, he questioned Whipple repeatedly about her position on tax issues.

During his years on the board, he said, he has been guided by "my concern for the overtaxed single-family homeowner" and charged that previous Democratic majorities "delighted in creating new and unnecessary ways of spending the hard-earned dollars extracted from the pockets of the taxpayers, regardless of their age, ability to work or amount of income."

He said the property tax rate could not have been reduced from $1.45 to 98 cents per $100 of assessed value with the increases in spending for schools, Metro and other programs that Whipple would have supported had she been elected in l979.

Whipple disagreed, arguing that additional taxes to help fund Metro, increased state aid to the county and an increase in Arlington's tax base still would have permitted the county's tax rate to drop.

She also said Detwiler's vote last March to raise the county's 96-cent real estate tax by 2 cents was politically advantageous to him because it avoided significant program cuts.

At the time, Detwiler reluctantly voted with the board's two Democrats to raise the tax rate, saying the old rate would provide insufficient revenue for contingencies. After that vote, Detwiler said he would propose a midyear tax cut if the fiscal picture improved, a preelection action Whipple called politically motivated.

The issue Whipple raised most often was what she called the "back-room firing" of the county manager last August, which she contended violated the tradition of open government in Arlington. She argued that the Republican majority has not been sufficiently open about its actions and decisions and cited Ford's firing as the prime example.

When she asked Detwiler why he did not consult with the full board when he told Ford to resign or be fired, Detwiler replied that he brought the issue before the board 48 hours after meeting with the manager to discuss the situation. Board member Ellen Bozman was not present, he said, because she had to leave the meeting early.

"There were continued discussions over more than a month's time after that before any decision was made, and that decision was made in public with the full board participating," he said.

Whipple, a former school board chairman, stressed her managerial and fiscal experience on the school board and criticized Detwiler's support for cuts in school programs.

When Detwiler said the fiscal 1983 school budget is $1.5 million above County Board guidelines, Whipple replied that the spending guidelines set by the three Republican members of the County Board were arbitrary, and that the schools were alloted $1.5 million less in county funds than was necessary to maintain current programs.