The answer is contained in a sordid tale of professional malfeasance, undisclosed conflicts of interest, and unmitigated avarice inflicted on the public by various interests, chief among them the sugar industry, desperate for a way to exonerate itself for fueling cavities in the population.

The fluoride-pimping project dates all the way back to 1930, nearly a hundred years ago, following the founding of a "nonprofit" industry front group called the Mellon Institute of Industrial Research.

Via Carnegie Mellon University (emphasis added):

"The Mellon Institute of Industrial Research was a non-profit independent research firm, dedicated to solving the immediate research needs of industry and training new scientific researchers for the benefit of society as a whole. The institute was established in 1913 with financial support from Pittsburgh financiers Andrew W. Mellon (1855-1937) and Richard B. Mellon (1958-1933). Originally founded as the Mellon Institute of Industrial Research and School of Specific Industries at the University of Pittsburgh, it was the first major research firm of its kind in the United States. In 1927, the institute separated from the University of Pittsburgh and incorporated as an independent, non-profit organization that was managed by a board of trustees. It also changed its name to Mellon Institute of Industrial Research.

The 'industrial fellowship system' – the framework behind the institute – was conceived by Robert Kennedy Duncan (1968-1914), a chemist and professor. The fellowship system promoted strong partnerships between industry and scientific research; it also educated new scientists and exposed them to the real world of industrial research…

Fellowships were sponsored by a wide variety of companies and individuals such as the Armstrong Cork Company, American Iron and Steel Institute, Gulf Oil, H.H. Robertson Company, Union Carbide, and the St. Joseph Lead Company."