Three things that make coaching work...

Intent = having the client's best interests at heart, maintaining focus on the client's own goals and also being aware of what you gain from coaching so it is a fair and equal exchange.

Perspective = you see the client's situation in a different way - just from the outside, or at a different level or whatever. The key is that you are not bound by the client's rules and doubts about what won't work.

Relationship = a medium through which communication can take place. This means both listening properly, and also being able to give feedback that resonates and is accepted rather than bouncing off the client's defensive shield.