What happens when the spoilers get deployed? All of a sudden, the lift is killed on the upwind wing, all four MLG tires 'bite' the runway surface, and the airplane immediately follows its heading, which, as you remember, was to the left of the runway heading.
Well almost. Classic 737's have a pivot on the MLG which is why they crab when they taxy. That would have alleviated the effect that you describe.