It’s based on your feeling and understanding of the world. As the GM, you are entitled to say: Sorry, Suasion is not appropriate here. This guy hasn’t bought into your system of beliefs. Test Rhetoric (or Persuasion or Soothing Platitudes or whatever is appropriate to how the player described his action) instead.
The important thing though is to be consistent. If that’s your ruling then make sure to follow the same ruling later on.
And just to be clear, you would also be justified as GM in deciding that yes, Suasion does work or even as others suggested that applying an Obstacle penalty is appropriate. It really depends on how things work in the setting you and your players have established.