What is the difference between contravene, contradict, and controvert?

All three words come to us from Latin, combining contra (against) with venire (come), vertere (turn), and dicere (say). Thus all three have a sense of opposition:

• Contravene: infringe, come in conflict with, dispute. This usage is applied to violating a law or abridging someone's rights.
• Contradict: to say the contrary or to be directly opposed.
• Controvert: to engage in a dispute or make something a dispute, oppose

The OED quotes British biologist Thomas Huxley (the defender of Darwin's theory of evolution):

Are those conclusions so firmly based that we may not contravene them?

In this instance, contradict or controvert would make equal sense, but they are not always interchangeable:

• Only contravene will do for the violations against, as in

  Serbia contravened the European Declaration of Human Rights

• It is possible to dispute (controvert) a position without making arguments that directly oppose (contradict) it.
• Only controvert has an intransitive use:

  Quakers do not controvert among themselves

• Only contradict has a figurative use:

  Your arrogance contradicts your protestations of humility.