Andrews and Petsche formulated a conjecture that an arboreal Galois extension is abelian if and only if the polynomial is conjugate to a powering map or a Chebyshev map and the base point is a root of unity in a number field. In this talk, we will discuss if a rational function is postcritically finite, and the base point is not preperiodic, then the arboreal Galois tower is not abelian. This uses two deep theorems, a result by Benedetto-Ingram-Jones-Levy on attracting cycles, as well as an equidistribution result by Baker-Rumely, Favre-Rivera-Letelier and Chambert Loir. This work is jointly by me and my advisor Clayton Petsche.