Jeremy also hints at something that I think gets lost a lot, and that being how we perceive racial ability score adjustments. I.e., we see "Elves get +2 Dex" means that all elves, or elves in general, are more dexterous than anyone else. Instead, it actually means, "YOUR character who is an elf is more dexterous." When you change your perspective from "most races like X" to "my character gets this as an individual", it's much more easy to accept how a dwarf might be a wizard, or a halfling is extra strong. Because it's about your PC who is an exception, not a modifier to the average halfling, or elf, or dwarf.