How can the word "dispatch" be spelled "despatch" and still be correct?

Same reason as very many alternative spellings.

Because some people in some places spell it that way.

"There is no difference between dispatch and despatch. The latter is an alternative spelling that was common in the 19th century and earlier, but dispatch has gained undisputed dominance in modern English. Despatch has mostly disappeared from the language—except in the U.K., where it appears in place of dispatch about a third of the time—and dispatch is the preferred spelling for all senses of the word."

The English language (outside of actual England) is full of examples like that. There are rules but there are a bunch of exceptions. Then why are there rules in the first place?