There are literally a number of books dedicated to answering this question.

The short answer (but I hate the short answers since it over simplifies what happens) is that, in trying not to favor one side or the other, Captain Kidd took a couple of ships that he shouldn't have, which means he took them piratically. As a result, he was brought back to London and tried for piracy (because the situation with trade in the Indian Ocean was delicate and some people didn't want to pass up bashing their political opponents who had funded this privateering expedition under Kidd in the first place - it takes a lot of money to pay for the vessel, supplies, armaments, and the security to be paid so as to try and assure that privateers behave according to the law). Now, there are plenty of questions here - Did Kidd intend to be a pirate from the beginning? Did he intentionally engage in piracy when taking those two prizes or was he really believing that the French passes that were on them made them legitimate French prizes (since his commission allowed him to take on enemies of the state of England at the time, which included France)? Did his crew force him to become a pirate?

There are plenty more questions that could be asked of this case - but I would recommend reading a book on the subject rather than trying to get a Reddit reply or a wikipedia article to answer them. If you want the best researched and argued text on the subject (rather than one not so heavily biased by pirate romanticism and errors made by people who aren't as well trained with history studies), the only choice is Captain Kidd and the War Against the Pirates by Robert C. Ritchie. It's the only publication I know of relating to Kidd to come from an academic press (and get peer reviewed by academics), Harvard.