Why did the federal reserve allow interest rates to rise in 1979?

the problem was that the economic expansion of 1975 continued and in 1979 the economy had the risk of generating inflation and because there was the risk of inflation the government had to take measures to reduce it. One of this measure was increasing interests so money was more expensive since the interest rate is the price of money. The Banks reduced their demand of money and at the same time they had less money to lend and this reduced the monetary supply which eventually reduced inflation.

Explanation: Part of the trouble was that the post-1975 U.S. economic expansion proved to be more robust than had been supposed; moreover, the Federal Reserve's deflationary stance seemed to the rest of the world unconvincing. So in the end the American boom had to be publicly and unmistakably decapitated. This was done on October 6, with all the appropriate gestures, by Mr. Paul Volcker, who had taken over the chairmanship of the Federal Reserve System a few weeks earlier.