This question presupposes agreement with this statement. As such, my first inclination was to find a context in which I agree with it. Ugly may be defined at first pass as diverging from the traditional aesthetic or values of the audience, and beauty as touching on this sense of aesthetic or values in a fundamental way. Ugly generally has negative associations, beauty positive ones. The terms are highly subjective and audience-dependent, so societal definitions of the terms may be difficult or impossible. They remain intensely personal in interpretation.
In art, intentional ugliness may occasionally be considered beautiful for its originality and interest, for focusing an aesthetic discipline on something not conventionally considered aesthetically pleasing to the senses. In an abstract sense, ugly may be beautiful for the thought and discussion it provokes. Unintentional ugliness in art, though, may be artistic failure or simply a matter of audience.
In real, personal experience, the opposite is true, and intentional ugliness is unlikely to achieve beauty in any sense of the word, such as an ugly emotion that parlays into an intentional, ugly action. But unintentional ugliness in life may often be beautiful. Ugly in physical appearance may be beautiful, for it may betray beauty in another sense, in a human face it may be an expression of the inner spirit, or the sad and regal beauty of wisdom gained through suffering. A well-loved, old, worn stuffed animal, or a chipped, stained mug, may be both ugly and beautiful; it has given joy and served a positive, constructive purpose. That object brings back positive associations to its most frequent audience.
So why is ugly beautiful? For those cases where this statement holds, ugly is beautiful because it at once stimulates a negative association for one audience and a different, positive association with the sense of aesthetic or moral values of the same or another audience.
— K. Alexandra Curtis, Postdoctoral Fellow in Fisheries Oceanography, Memorial University of Newfoundland, Canada