It's kind of an interesting question, that has a number of layers. Before answering more directly, here's a key point:

Passive-Aggressiveness Not Usually "Intentional" or Conscious

It's easy to label a person who often uses passive-aggressive techniques as nasty, stupid, intentionally manipulative, or apply any number of different negative words to the person. The problem is that when you apply those labels, you don't get a better relatinship.

In fact, passive-aggressiveness is a learned habit that people learn quite early in life. As with many habits' it gets triggered in a way that is relatively automatic, like any other strong habit (e.g. tapping your fingers, clearing throat, nail biting). To make the point, nail biters don't sit, and DECIDE to bite their nails. They just do it out of habit. 

In the same way, most passive-aggressiveness comes from the same place. It's not usually thought out and intentional. That's doesn't means it's never intentional, but mostly it's habit that comes out for that person under certain specific situations.

So, Why?

The over-riding reason is that we all learn that arguments, and direct expressions of anger can have quite unpleasant short term results. We tend to forget that long term, it's better to solve problems than to hint about them, or pretend they don't exist. One reason the unpleasant results happen is that we are not very good at teaching both young ones and adults how to resolve disagreements, anger an hurt feelings.

Another way of putting this is that in situations where a person is using passive-aggressive techniques, it comes from a sense of fear of direct expression. That fear may be warranted if the relationship has a terrible history of horrible arguments, or oddly enough, it may be based on relationships long past. Or even back to childhood.

If you think of passive aggressive behavior as coming from someone who is frightened, you'll be much better able to turn the situation around into something constructive.

A lack of communication skills is another cause. Often times, people act in passive aggressive ways because they don't know how to do otherwise. The skills needed to openly address relationship problems, and upset are quite advanced, and historically, we haven't taught people how to do this. So it's not surprising that people use the skills they have, which often have to do with sniping, denying upset, and so on.

The Good News About YOUR Passive-Aggessive Behaviors

There's good news when it comes you YOUR passive aggressive behavior. Since the causes have to do with fear, with lack of skills, you can learn new and better, more constructive skills, and increase your own awareness of how you behave when you are upset. Passive aggressive behavior is learned, and can be unlearned. Conflict resolution skills can be learned.

Focus on YOUR use of passive aggressive techniques, and CHOOSE to eliminate them one by one, and try to step out of how you usually interact when upset. The first step to a more constructive relationship and handling of anger is to START.