It strikes me as a too emotional attitude. Nani has a contract at the moment, it's not like he's unemployed. If he doesn't want to renew, then you either give him a better contract if you want to keep him, or you try to maximize your winnings by selling him while he still has value, namely in January or the next Summer window.
In the meanwhile, if your wingers are out of form and Nani can do a better job than them it's daft not to make use of him. The only thing you accomplish is to lower his potential value and harm his career. All that to... make a point?
This opinion is based on what we know about the situation. I reckon there may be more strings attached to it that could make me change my mind. But to me, a player not wanting to sign an extension (it's his damn right if he's not happy with what he's offered) doesn't mean he's lost his use at the club. He's still got two years ahead of him employed by the club, and two transfer windows on which he could be sold by a good sum.
How you can defend SAF in this decision is also a bit of a blind following. He may even be right, with the information we don't know... But as you put it, if that's the only reason Nani is not playing, than it's an attitude that benefits no one and harms both the club and the player.