The neutron skin of atomic nuclei impacts the structure of neutron-rich nuclei, the equation of state of nucleonic matter, and the size of neutron stars. Here we predict the neutron skin of selected light and medium-mass nuclei using coupled-cluster theory and the auxiliary field diffusion Monte Carlo method with two-and three-nucleon forces from chiral effective field theory. We find a linear correlation between the neutron skin and the isospin asymmetry and compare with data. We also find a linear relationship between proton and neutron radii of mirror nuclei and quantify the effect of charge symmetry breaking. Our results for the mirror-difference charge radii and binding energies per nucleon agree with existing data.