One motivation why a photographer would choose a background of black and white or grayscale would be to accentuate the subject of the photograph. Black and white photography helps to focus the viewer's attention on the subject. Photographer Vincent Versace suggests as much:
“If I had my druthers, I’d never shoot another color photograph as long as I live.” That is because without color to “distract,” he said, a photographer has to learn composition and the skill of capturing a story.
This is one potential motivation of a photographer choosing a background of black and white or grayscale. The centrality of the subject is where black and white photography is able to tell a story in clear detail, impacting the viewer. When one sees "Migrant Mother" by Dorothea Lange, its black and white quality tells the story of harshness, sadness, and a condition in which photography becomes its own art form.
Another similar reason for choosing a background that is devoid of color could be to provide tonal contrast. For example, a subject in a black or white uniform could be the subject of an interesting photographic experience with contrast if the background is grayscale or black and white. The focus is on the subject, as before, but black and white backgrounds help to focus attention on the tonal quality of the photograph, something that is not as readily available with a color background.