School closings have become among the most controversial and resisted steps in the suburbs in recent years, but two groups of parents -- one in Arlington and another in Fairfax County -- asked school officials last night to close their schools.

In Arlington, parents of children who attend Woodmont Elementary asked the school board to close that school and merge it with nearby Taylor Elementary next year. The proposal, which the Arlington board will consider Dec. 17, drew strong opposition from parents with children at Key Elementary, also near Woodmont.

In Fairfax, PTAs representing the Lewinsville Elementary School and Kent Gardens Elementary, both in McLean, asked their county school board to close Lewinsville and transfer its pupils to Kent Gardens. They noted that enrollment at both schools has been declining and cited the probability that one of the schools would have to be closed anyway. The board was receptive and no opposition was apparent, although no decision was made.

The action proposed in Arlington was outlined by representatives of the Woodmont PTA, whose merger proposal has been endorsed by the Taylor PTA. They cited rapidly decreasing enrollment at Woodmont and the probability of its eventual closing as elementary school reorganization is implemented in the next two years.

Woodmont, built in 1972, has 204 pupils, but its projected enrollment next year is only 165. The school board's policy is to require elementary schools to have at least 222 students.

The proposal was attacked by Key school parents who said they fear a merger would weaken the stability of their schools, which has a transient student body, 60 percent of whom are non-English-speaking.