Why is Judge Judy so harsh?

In part, she tries to run her TV show the way a real court would operate; testimony must be direct and in response to questions. This is far more strict (and realistic) than some other court shows on television, which permit litigants to tell long stories containing lots of irrelevant, unprovable details, slander and doubletalk.
Second, she uses intimidation as a tactic to get litigants to perjure themselves. Once she catches them in their own lies, she can make a ruling without having to dig into a lot of details.

Finally, she really has little patience for fools, and none at all for crooks. In many cases, she has a pretty good idea of what the litigants were trying to do, by reading their complaints and police reports, before hearing their testimony. She has seen just about everything in her career and she understands human motivation, so she can tell if one or both of the litigants got into their situation by trying to do something illegal or underhanded. She will usually question individuals like that aggressively from the outset.