While you already accepted a very good and quite detailled answer, let me try to add another one, commensurate to the level of the question:
What kind of security control would cause a breach of privacy?
"Security" has, amongst others, these uses:
- Protect some information from being seen by any but the intended parties.
- Prove the identity of one of the intended parties to the others (authentication).
- Prove that one of the parties is allowed to do or see something (authorization).
- And plenty of others.
In many cases, authentication and authorization do not necessarily need to go together to make a system work as intended. If a security control manages to handle authorization without authentication, then, great!
Examples:
- The infamous example of the (real or fictional, I don't know) Swiss bank which lets a customer into their vault only based on them knowing some secret password (not their identity). The security control is simply the knowledge of the password.
- A user of a leased car with a payment card for gas can use that card, together with a PIN, to pay the gas bill, without the identity of the user playing any role (here, the security control is the combination of physical possession of the card, and knowledge of the PIN).
- Modern schemes like OAuth or SAML make it possible for an application to let only privileged users in without knowing anything about those users. For example, you can log into a random small web site using your Google or Facebook account - the web site does not need to know anything about you as a person; it can trust Google's or Facebook's account database that it's really you. This scheme is a little more involved, it has different systems with different roles (i.e., keeper of your private data; keeper of the information that you have access to some resource; and a system for checking that from the point of view of a 3rd party app; these can be very different systems, so in theory not even the keeper of your private data gets to know which apps you are working with by separating out the system that matches that stuff).
To circle back to your question: any security control which is not like that, in spirit, would breach your privacy. If you have to give your personal name, audibly, at the doctor's office, then everybody around you will know that you have a reason to be at that doctor. If you need to give your real name whenever creating an account at a website, preferably with your bank information too, then that web site has a nice little collection of data about you, that it absolutely would not need otherwise. If you had to give your real name to the Swiss bank, it would make it much harder for you to manage your hard earned money without having to pay pesky taxes... and so on and forth.