"Só para contariar could be "just to give someone a bad time".  The word "just" is very important in the phrase because it indicates that you are teasing someone, pulling their leg, having fun with him.  You are not trying to hurt, insult, offend, or humiliate him."

Spot on description, Dale.

Sometimes is the tug-of-war teens and his parents, teacher, adulsts, get involved, tough they doen´t meant to offend.

But other times is the things wives (and hubbies too) do only to reaffirm their authority, a power struggle.  Say, the wife let the house a mess "só pra contrariar", since his hubby said she don´t do much at home, he is the one that works!

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She went to the party only to bug her parents.

Ela foi a festa só pra contrariar (seus pais. )

He likes socialise with the annoyng guys next door, right the ones his parents don´t approve of.

Ele gosta de interagir (conviver) com a turma dos garotos irritantes/aborrecentes/desagradáveis da vizinhança, justo aqueles que os seus pais disaprovam.

She talks back only to exasperate and let her folks umcomfortable, but deep down she loves them.

Ela responde mal só pra contrariar (os seus velhos), mas no fundo no fundo ela os ama.

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Other sense:

There´s the case of people that do something (generally good things) only to prove that those that say they won´t succeed wrong. 

That is, by sheer obstinacy, they fight back and win.

The former president Lula run for Brazil´s presidency for seven or more times, even knowing that the odds were against him, he wouldn´t never win! But he won at last!

Nelson Mandela was president of South Africa, só pra contrariar. (only to prove history wrong! Hehe)

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Other times só pra "contrariar" would mean an irony of destiny (kinda "who would imagine that...?":  

- No século 20, os estados Unidos teria Obama, um presidente negro, só pra contrariar! 

- Só pra contrariar, o Lula lançou uma candidata à presidência, e ela ganhou!

Notice, that is said in an almost humourous, musingly way, not pejoratively here. 

I don´t have a terse definition to these two, but I bet Dave and others will have.