"Friendships, like marriages, are dependent on avoiding the unforgivable"

The author is saying that in order for a friendship to be successful, it is important to avoid doing something that is unforgivable. Essentially, if someone were to do something genuinely incorrect or upsetting to a good friend, it might damage the friendship irreparable. The same goes for marriages, where unforgivable acts can result in incurable damage and also possibly completion of the connection.