I once read somewhere that siblings (in this case brothers) have something inherently similiar to their voices which is what renders a unique harmony sound which cannot be duplicated by non-siblings. It applied to the Beach Boys, the Bee Gees and the Everlys as well as others.
Additionally, wiki says this about the Everly's harmony...
Don and Phil Everly, both guitarists, used vocal harmony mostly based on diatonic thirds. With this, each line can often stand on its own as a melody line. This is in contrast to classic harmony lines which, while working well alongside the melody, are not as melodic by themselves.
On most of their recordings, Don sings the baritone part and Phil the tenor part. One exception is on "Devoted to You". Although Don is still low and Phil high, they switch lead and harmony back and forth. Don typically sings any lines that are sung solo (for example, the verses of "Bye Bye Love"); among the exceptions to this rule is the 1965 single "It's All Over", where Phil sings the song's solo lines.
In the late 1950s, the Everly Brothers were the rock 'n' roll youth movement's addition to close harmony vocal groups of which many were family bands. The duo's harmony singing had a strong influence on rock groups of the 1960s. The Beatles,[1] the Beach Boys[2] and Simon & Garfunkel developed their early singing styles by performing Everly covers. The Bee Gees, the Hollies and other rock'n'roll groups that feature harmony singing were influenced by the Everlys.