Fight shy of something/of doing something
Definition 1 of 1
Pro Tip 1/3Emotional Avoidance
Indicates avoiding something due to negative feelings rather than practical reasons. 
I fought shy of visiting the dentist after a painful experience.
Pro Tip 2/3Subtle Discomfort
Implies a quiet, internal discomfort, not always visible to others. 
He fought shy of discussing his salary, even though it bothered him.
Pro Tip 3/3Situational Context
Best used when referring to specific situations or topics one wants to avoid. 
Sarah fought shy of the topic of marriage whenever it came up.