Ballou High School teacher Emily Washington entered the building recently and found an anxious parent waiting at her office door with a single purpose. "I want to know if you will let my son march in graduation," he said.

His son, like an estimated 2,100 Washington-area high school seniors, will not graduate this school year. And teacher Washington was facing the other side of graduation time--pressure from parents and students to raise grades, give second chances or allow their children to "march" with their graduating classmates even if it means receiving only a blank sheet of paper.

"Graduation is a tough time for parents, teachers, students and administrators," said Carl Hymes, principal of Roosevelt High School in the District.

Some failing high school seniors quietly resign themselves to night school or summer classes. Others plead, cajole and even threaten teachers who have given them the bad news. District school officials said one student became so upset after being told he was failing that he allegedly attacked an assistant principal with a trash can lid.

These reactions, teachers and administrators said, are as much a part of the end-of-the-school-year-tradition as "Pomp and Circumstance." They said they sometimes feel threatened by the pressure of students and parents and often agonize over whether they did enough to help students who failed.

"I feel sorry for those who failed, sorry for me that I didn't teach them more and sorry that they didn't know more," said Nancy Cox, a teacher at T.C. Williams High School in Alexandria. "This time of the year there is always some day when I go home and say to my husband that this may be the time I give up teaching for a while . . . . But I've been teaching for 25 years and I've learned finally that you really can't carry them all."

In the District, one out of every six seniors, 792 out of 4,626, failed to graduate this year. Figures for other Washington-area jurisdictions are not yet compiled for the class of 1983, but 562 of 8,739 Prince George's County seniors did not graduate last June. Another 411 out of 10,545 seniors in Fairfax County, and 299 out of 8,072 in Montgomery County did not graduate last June.

All Washington-area jurisdictions have procedures for notifying the parents of high school seniors several times throughout the year to let them know if their children are in danger of failing required courses. In the District, for example, parents receive deficiency notices prior to the first grading period. In the middle of the fourth grading period, students are sent potential failure notices, said Hymes.

Despite usually elaborate and thorough notification procedures, decisions on who will not graduate never fail to bring disputes.

One senior at T.C. Williams, school officials said, suffered a collapsed lung in a car accident that prevented his attendance during the last five weeks of school. Although most of his teachers waived his final exams because of the accident, one didn't and the student did not do well enough on the exam to pass the course. He will have to retake the course next fall.

"It was upsetting, but I guess that's the way it goes sometimes," said the student who asked not to be named. "I had planned to go to Northern Virginia Community College next fall . . . . Now I will go to night school and work during the day."

After Joseph Reeder was told he would not be allowed to participate in Ballou High's recent graduation ceremonies because of poor performance, he allegedly assaulted an assistant principal with a trash can lid. Reeder, a 19-year-old who faces misdemeanor charges of assault with a deadly weapon and threats of bodily harm as a result of the incident, declined to discuss it.

The end of the school year, said one Ballou High social studies teacher, often brings harassment to teachers. "It results in emotional tantrums on the part of students," she said. "It's extremely stressful. Parents can complain that they never received notices in the mail."

But other teachers describe a different sort of dilemma.

Ballou's Washington, a former City Council and school board candidate, and Pat Brown are two of the Ballou High English teachers who administered standardized reading tests to the senior class. Thirty tested below sixth-grade level, they said. Another 162 fell between the sixth-and eighth-grade levels.

"Some want to go to college," said Brown. "Some want to enter the work force and you know they are not going to be able to pass entrance examinations. You become the keeper of the gate. If you take pride in your work, you don't want them thinking that they are equipped for the dreams they have."