Separation energy of nucleons and Coulomb barrier

My professor and the book I'm reading (Particles and Nuclei: An Introduction to the Physical Concepts by Povh et al.) says that "The emitted nucleons are primarily neutrons since they are not hindered by the Coulomb threshold" which means that a neutron has a separation energy lower than a proton. They take this as true, indeed for example when a nucleus decays to another nucleus in an excited state, we compare the energy of this excited level and the separation energy of neutron to check if it's bonded for nucleons' emission (like in the ##\beta##-decay
##^{60}_{27}##Co ##\to## ##^{60}_{28}##Ni).

I still don't get how, although the Coulomb force between protons is repulsive, the existence of this force makes it harder to separate a proton from a nucleus. I'd expect the proton to see something which reduce the confinement inside the well (of the nucleus) but this is not the true, it sees a barrier caused by this force. Instead a neutron doesn't see a barrier because there's no Coulomb force and therefore (I guess?) it's easier to separate.

So, why the Coulomb force, which should facilitate the separation as it's repulsive, makes it harder for a proton to be separated than a neutron?

However, my professor gives an explanation which I really hate (or maybe I don't understand?). She says that to understand this, you have to see the process in time-reverse, which means the proton that "enters" the nucleus and of course it meets a barrier. Then something about conservation of the energy in the reverse process and that's it.

If isotopes are stable against beta decays then p -> n + e+ has to be forbidden. In that reaction we would gain energy from the positron leaving the nucleus, that means the highest filled proton energy level has to be lower than the highest filled neutron energy level, otherwise you would get beta+ decays. How much lower is given by the Coulomb potential.