Why are brussels sprouts and tomatoes incompatible in the garden? How far apart must they be?

I have a small kitchen garden, 8 ft. x 16 ft. the 8 ft. being the southern exposure. I plant tomatoes in tall 5 ft. cages on the north end and plant grading to the shortest plants on the south end. The sprouts normally get less than 3 ft. so I intended to plant the 1 that I have (spaced about 2-3 ft. from one of the tomato cages). I've since heard that they should not grow together at all lest both plants suffer. Does anyone know why this is so and what I can do to correct the situation without removing the brussels sprout plant? I had sprouts last year but they were 8-10 ft. away from the tomatoes. No problem.