This is due to the Sports Broadcasting Act of 1961: the NFL is legally forbidden to televise any matches on a Friday night within 75 miles of any high school during the high school regular season, and similarly for Saturday nights and colleges. As virtually the whole of the USA is within 75 miles of a high school or college, this means they couldn't televise the match at all - and as the NFL's money comes from television broadcasts, that's a huge deterrent not to play.
Once the high school and college seasons end, the NFL is free to play on Fridays and Saturdays, which is why playoff games happen on a Saturday.