Passive-aggressive people learn from an early age to supplant authentic self-expression with a façade of niceness and accommodation. They have been taught to please others rather than themselves and to sacrifice honest communication for conflict avoidance. As a result, they have a hard time expressing themselves and exerting influence over their lives. Because they feel so powerless and at the mercy of others, and because they cannot overtly challenge or change their oppressive predicament, they tend to act out in a "passive-aggressive" manner, by being chronically late, for example, or "forgetting" for the tenth consecutive month to pay their portion of the rent check.
If you want to stop being passive aggressive, my suggestion is that you practice asserting yourself and being more direct with the people in your life. For example, if your friend asks you yet again to take care of her cat while she goes to Club Med for her annual holiday free-for-all, and every year you've accepted but secretly seethed with resentment (and then occasionally "forgot" to feed Molly the Maincoon), I suggest you try a different approach this year. Muster all the courage you can, and tell your friend that you'll be unable to take care of Molly this year. You don't have to lie about why or even give her a reason because, ultimately, you have a right to say "no" regardless of your reasons and your true friends will respect that right. Yes, they may not like to hear your "no," especially when they have learned to count on you to say "yes, yes, yes" all these years, and there may be moments of conflict that ensue, but any relationship worth having can weather those conflicts.
Passive-aggressive people often fear that if they set boundaries or directly express themselves they will be rejected or will create some kind of conflict that they feel ill equipped to handle. Because they avoid such authentic encounters and hide behind a façade of pleasantness and accommodation, they never learn to handle the understandable and necessary conflict that is part and parcel of all normal relationships. Eventually, their aggression is bound to blow up and create the very antipathy and rejection they so dread.
So try to exercise a new muscle of truth telling, and you'll reap the benefit of more solid and authentic relationships.