err on the side of (something)
To prioritize something, perhaps excessively or unnecessarily. Often used in the phrase "err on the side of caution." I like to err on the side of caution and always keep some money in my savings account.
err on the side of
act with a specified bias towards something. 1999 Nature Der Sündefall's message may err on the side of alarmism, but it certainly is a good read.
err on the side of something
show slightly too much rather than too little of a quality, especially a good one: When I am marking exam papers, I always try to err on the side of generosity (= I give slightly higher marks than the students may deserve). Err is an old-fashioned word meaning ‘make a mistake’.