Again in the second proverb of this pair there is a contrast between straightforward faithful dealing between friends, and a fake friendship that pretends affection but is never able to do the hard things that needs to be done. It substitutes what it thinks is a show of affection for the real thing.
Those who receive admonition need to learn to see beyond what is presented at face value, and read in their friends faithfulness what is a true loving response. It takes wisdom to receive admonition as well as to give it. In order to receive correction we may need to accept that others understand what is good for us better than we do ourselves. This is unavoidably humiliating because we ought to understand this better than anyone else. Instead we have been forced to temporarily relinquish control of our lives to another.