The primary issue is the availability of space station docking ports fitted with an "international docking adapter," which are used by SpaceX's Crew Dragon, Cargo Dragon 2, and Starliner vehicles. There are presently two such ports on the station, and for NASA, the priority for access to these ports are crew rotations followed by supply missions. So the question becomes when the Starliner test flight can find an open slot on station.
The Crew-2 mission, carrying four astronauts on SpaceX's Crew Dragon vehicle, is expected to launch on April 22 and remain attached to one of these ports for about six months. Then, on June 3, a SpaceX cargo supply mission (CRS-22) is due to launch and occupy the other port.
Thus, there will be no docking ports available this summer until about July 20, the approximate date when the CRS-22 Dragon will depart the station and return to Earth. This departure will open an approximately one-month window during which Starliner could make its test flight. Therefore, although NASA and Boeing have not yet made a target date public, we can expect this flight to take place no earlier than late July or early August.
[...] After this repeat test flight, which is officially known as Orbital Flight Test-2, NASA and Boeing will perform a detailed data analysis. One source said that optimistically, this process would require about six months. This would push a crewed test flight into January 2022. Another NASA official said the spacecraft would not fly until the "hardware is ready and it makes the most sense to fly based on station's needs." He added that there is no clock on this crewed flight test, since NASA already has an operational vehicle, Crew Dragon, to meet its astronaut-rotation needs.
[...] Finally, if this crew test flight is successful, Boeing could fly its first "operational" Starliner mission for NASA. This would carry a full complement of four astronauts to the space station for about six months and would happen sometime later in 2022, most likely during the April or September time frames.