Why are elements with even atomic number more abundant?

I will add to the answer from @BowlofRed https://physics.stackexchange.com/a/158270/36194 that the nuclear pairing interaction lowers the energy in nuclei where the number of like nucleons is even: thus for instance there are more isotopes with even rather than odd number of neutrons. This also favors the formation of even-proton-numbered nuclei over the neighbouring odd ones.

The binding energy of a nucleus depends on the pairing status of the protons and neutrons. In particular, in the semi-empirical mass formula, there is a pairing term which captures the mutual interaction associated with the energetic favourability of pairing nucleons with opposite spin. That means nuclei with even numbers of protons and neutrons have higher binding energies than those with odd/even and especially odd/odd nuclei.

What this means in practice is that there is an energy penalty and therefore a reduced probability of producing elements with odd numbers of protons during equilibrium nucleosynthesis reactions inside stars.

For example a heavy nucleus with an odd number of protons might be more likely to undergo beta decay if it is neutron-rich or more likely to undergo neutron capture if it is neutron poor, than an adjacent nucleus with an even number ofprotons.