I had long assumed it was for budgetary reasons. If I recall correctly, I had even read somewhere something to the effect that to meet their budget for whatever fiscal period, Disney had to cut color from one of their productions, and THE ABSENT MINDED PROFESSOR (1961) ended up being it.I was surprised as well when somebody claimed The Absent Minded Professor was in color. I believe it was done specifically in b and w because this would conceal the special effects better, I assume such as the wires used in the basketball game.
However, this article bears out Roxy's explanation:
It now occurs to me it might have been THE SHAGGY DOG (1959) that was shot in Black and White due to budgetary constraints.