Single word **or phrase** for somebody who feigns deafness when contradicted?
We often say something like "Henry has selective hearing." This is often followed by "He only hears what he wants to hear."
While selective hearing might describe a clinical problem (also referred to as selective auditory attention), it's a common expression.
The clinical explanation suggests it is not voluntary, but in common usage, observers generally suggest that it is deliberate. It can be used (perhaps half jokingly) when referring to an aging spouse who may appear to be hard of hearing, but miraculously is able to hear some things that others might not expect to be heard. However, age is not a necessary part of selective hearing, as many teenagers are accused of it, also.
At Urban Dictionary, it is explained this way:
one posseses this quality when they hear only what they would like to hear.