This work uncovers an essential dual-phase structure of identical particles, revealing a fundamental limitation in existing quantum statistical theories. For a considerable period, it was commonly assumed that an interchange of two particles would be accompanied by a fixed phase factor. Here, the author discovers that the exchange process inherently involves two distinct phases: a relative phase α and an exchange phase β, rigorously related through α = β-1 = e±iθ. Specifically, α = β = 1 characterizes bosons, while α = β = -1 describes fermions. This finding necessitates a radical change in handling identical particles. Within this new framework, clockwise exchange yields α = eiθ and β = e-iθ, while counter-clockwise exchange gives α = e-iθ and β = eiθ. Crucially, both scenarios, despite their topological differences, are physically equivalent, governed by the universal constraint αβ = 1 for all identical particles. This framework not only fundamentally changes the conceptual basis of quantum statistics but also provides critical theoretical constraints on the existence conditions of non-Abelian anyons in two-dimensional topological systems.