There is no official or practical reason not to wear white after Labor Day. For many years it was considered a fashion faux pas in etiquette, but the origin of the unofficial rule is murky with several explanations proposed.
One possible reason is that white clothing reflects sunlight more than darker colors, thus making it a good choice to keep the wearer cool in the summer months. With rains and snow of fall or winter, white clothing was more likely to get stained with mud. Another explanation is that the upper classes favored lighter colored clothing when vacationing, and putting on darker and heavier fabrics symbolized returning to work in the fall. By the 21st century, the rule was considered outdated.