The thing about passive-aggressive behaviour is that it's not an illness or a psychological disorder, it's just a way of behaving, like being assertive, aggressive or submissive. It doesn't require a professional qualification to notice it and it shouldn't be pathologised or "diagnosed".
Like the other behaviours, all of us are capable of being like that some of the time. Problems are created in relationships however, when one or both parties has a default behaviour of being aggressive, submissive or passive-aggressive and behaves like this most of the time.
I see PA as communicating dissatisfaction and grievances in indirect ways and I think Flight's posts sum this up very well.
The person whose default is to be passive-aggressive often sulks, drops hints rather than communicate directly, withdraws from situations rather than confront them (but moans or carps on the sidelines), effects a martyr complex rather than saying "no", takes to their bed and hopes someone notices, puts obstacles in the way of going somewhere rather than saying they don't want to go, attributes their dissatisfactions to others ("It's not me saying this, but others have said...")
In argument, s/he regularly resorts to deflections such as "Well if you don't know what's wrong, I'm not telling you" or "You're right, I must be the worst Mum/wife/husband/Dad etc. in the world" or "Sorry if I can't be a paragon of virtue all the time, I'm sure I must be a huge disappointment to you." Followed by flouncing and sulking, of course....
You must notice it on here, when an OP is being a bit of an arse and people tell them so, quite directly but tactfully, only for the OP to come back and apologise for not being Mother Teresa and without sin?
Inwardly, respondents want to load a rifle and shoot the OP, but it would be tactless to say so and unfortunately illegal to do so, so we tell the OP to stop being so passive-aggressive with posters who have taken the trouble to respond.