(via Quora) Answered by Eric Johnson
Bob Dylan was in the middle of negotiations for the upcoming festival but backed out when his son fell ill and although he lived close to the upstate New York venue, legend has it that Dylan was so annoyed at the constant stream of hippies showing up at his door and accumulating outside of his house near the originally planned site of the festival that he turned the gig down and headed to England that August weekend of 1969. Two weeks later he did take to the stage at a music festival on the Isle of Wight in southern England.
Simon and Garfunkel were invited, but were “too busy” to accept. They were after all finishing up their Bridge Over Troubled Water album which was already over due. Garfunkel was juggling his time between the duo and his acting career.
The Woodstock organizers naturally did extended an invitation to the Stones to perform, however they were spread all over the place at the time. Their singer and band leader Mick Jagger turned the gig down on everyone’s behalf, and instead went to Australia to shoot a movie in which he played the outlaw Ned Kelly, that only a few even remembers now.
According to the book “Led Zeppelin: the Concert File” their manager said no because at Woodstock they’d have just been another band on the bill.”
In short, The Doors didn’t play Woodstock “because we were stupid and turned it down,” according to the band’s guitarist Robby Krieger. They thought it would be a second class repeat of Monterey Pop Festival of 1967.
Every Moment Has A Song 