This is very clear in split-brain patients where one side will make the decision and the other side will come up with an excellently reasoned explanation of the decision.
What's even weirder is that when the hemispheres are split apart, the two sides seem to both be able to understand and carry out instructions (and can even compete with each other to do them, e.g., the left hand and right hand may try to push each other out of the way), which suggests that there may be two wholly separate consciousnesses in each half of the brain.