First, the basic premise seems overstated at best. Folks cut down trees and replace them with other trees. More to the point, it is not unheard for redevelopment projects, even in urban areas, to create more green space.
Second, this tree hugging position is also overstated given that Brown's Chapel Park represents a little over one percent of Reston's open space -- 22 acres out of 1,700 acres. Placing an indoor facility on part of Brown's Chapel hardly represents the end of green space as we know it.
Most important, a thoughtful decision about a new facility requires an attempt to balance the possible benefits of a facility against what diminution of green space that might occur. If the community needs a new facility, surely it's possible that the facility's potential benefits would outweigh any harm that might come from clearing part of 22 acres.