If someone is cantankerous he has a difficult disposition. Take care not to throw your ball into the yard of the cantankerous old man down the street — he'll cuss you out and keep your ball.
The origin of cantankerous is unclear (it may be at least partly from Middle English contek 'dissension'), but ever since it first appeared in plays from the 1770s, it's been a popular way to describe someone who is quarrelsome and disagreeable. It is usually applied to people, but stubborn animals like mules are also described as cantankerous. Events can be cantankerous too, like a cantankerous debate. Some synonyms are cranky, bad-tempered, irritable, irascible.