To be clear, historically, many blamed Yoko Ono for the break-up of the Beatles. In the interview, she didn't see it that way. Instead, she blamed the split on the band members themselves, and specifically on Paul McCartney.
In the 1987 interview, Ono said:
The Beatles were getting very independent. Each one of them [was] getting independent. John [Lennon], in fact, was not the first who wanted to leave the Beatles.To be honest, the Beatles stayed together for a long time. Frequently, a band or group in which one person is more of a star than the others simply falls apart, as the superstar wants independence or creative differences take hold. Whatever the reason, one can look at groups such as The Supremes, The Commodores, The Go-Go's, The Bangles and more to see successful bands that couldn't stay together.
[We saw] Ringo [Starr] one night with Maureen [Starkey Tigrett], and he came to John and me and said he wanted to leave. George [Harrison] was next, and then John.
Paul [McCartney] was the only one trying to hold the Beatles together. But the other three thought Paul would hold the Beatles together as his band. They were getting to be like Paul's band, which they didn't like.
On the other hand, there are bands that have seemed to have stayed together forever, such as the Rolling Stones.
While many believe Ono lead to the Beatles' split, Ono herself said the group's break-up put a strain on her relationship with Lennon. She said that she believed that Lennon missed the band, and "expected all that to be replaced by me."
The release of the information, which came via the Joe Smith collection at the Library of Congress, is ironically timed. In October of this year, McCartney himself told David Frost that Ono "did not break the group up" because it was "already breaking up."
You can listen to Ono here (Part one, Part two).