If someone is crabby, small things annoy them. They snap, they complain, they are not in a good mood — but it is everyday annoyance, not deep anger. It is an informal home word: Don’t be so crabby. Calling a person crabby is a little teasing, not a formal judgment. You will hear it more in casual American talk; British speakers use it too, though grouchy or irritable may show up more in careful writing. It is milder and more everyday than furious, and it often points at tiny causes — the noise, the wait, the missing pen.