symmetry - Energy difference between enantiomers (matter/antimatter)

I am aware of the fact that enantiomers have different energies, for example L-amino acids have different energy than D-amino acids. The difference is not significant and is most usually about $10^{-18}$ eV. (1) Recently I have read that antimatter mirror images of compounds have actually the same energy. So L-amino acids will actually have the same energy as antimatter D-amino acids.

Can someone explain in relatively simply terms (meaning not too much math) why enantiomers have different energies and why matter-antimatter enantiomers have the same energy? Also if L is the more stable enantiomer for normal matter, will D be the more stable enantiomer for antimatter?

(1) Amino Acids and the Asymmetry of Life: Caught in the Act of Formation - Uwe Meierhenrich