It seems to me that "transparency" can be considered to be an antonym of "privacy". This isn't symmetric. Because few people would think of "privacy" as an antonym of "transparency". So where does the symmetry break down?
Edit: since the question is attracting some answers which address the title of the question, but are skipping the content of the question, I'll add an emphasis.
Emphasis: I am specifically asking "why does the symmetry break down?" Transparency is an antonym of privacy while privacy is not an antonym of transparency.
I freely admit that both terms have a lot of controversial uses attached to them. Most of the controversy is around where the boundaries of the terms lie and where they "should" lie. But in their basic usage, the lack of symmetry remains.