When two roads diverge, they split and go in different directions. If your opinion diverges from mine, we do not agree. To diverge means to move apart or be separate.
The poet, Robert Frost, wrote: "Two roads diverged in a wood, and I -/ I took the one less traveled by / And that has made all the difference." The word diverge in the poem carries both the meaning of separating and of being apart from the main. As a poet, it was Frost's job to use words properly. Here he does not diverge from this role.