“When an anxious recluse agrees to take his cancer-fighting friend on one last adventure, he doesn?t bank on having his beliefs, loyalties and survival skills challenged when she falls fatally ill.”(31 words)

The inciting incident of a logline, and a story, should be something that happens?to the protagonist, not something they do. It should be a specific, disastrous event that upsets the protagonist’s status quo and is outside of their control. Some examples:
Star Wars: When Luke’s family is killed.
Batman: When Bruce Wayne’s parents are killed.
Spiderman: When Peter Parker’s lack of responsibility indirectly gets his uncle killed.

In each of these an event outside of the protagonist’s control happens, and that event motivates them to pursue their goal. Unless I am misreading the logline, then the man is the main character.
“he doesn?t bank on having his beliefs, loyalties and survival skills challenged ” Isn’t a part of the objective goal, the action he takes. It is a part of the subjective obstacles he faces.
Another thing I see about the logline is that it doesn’t describe the journey well enough. What kind of adventure? Where? Why does she want to go there?

Example:?When his friend is diagnosed with fatal cancer, an anxious recluse takes her on a road trip across the country to visit her small town that she hasn’t seen in years.?(31)

I’ve tried to include my suggestions in my example. There’s a clear destination, and a reason she would want to go there. I describe the adventure as a road trip, creating a clear visual image.
I hope this helps.