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I am flying quite often, but never signed up for frequent flyer miles card. I am skeptic about my privacy. I also don't understand very well how frequent flyer miles work.

With a search engine I found almost no info about this topic:

The major airlines actually make more money with the frequent flyer
programs than they do as airlines. The market value of American
Airlines frequent flyer program is more than $6 billion -- the market
itself is $2.4 billion. What does it tell you? Airlines make a lot of
money by selling miles to their miles partners -- credit card
companies, banks, etcetera -- so you get a dollar for every dollar
you spend

I always register with my real name and credit card at the airline. They anyway have this data and can they sell it?

The main source of income for Frequent Flyer programs is not selling your information, but instead selling points.

Any time you earn points/miles from using a credit card that is affiliated with a frequent flyer program, the bank that issued the card has to purchase those miles/points from the frequent flyer program.

The same is true for any other programs that issue frequent flyer points, such as hotels, car rentals, etc - all of these require the person giving out the points to purchase them from the airline and/or the frequent flyer program.

If you fail to use those points within a set period of time they can expire, in which case that becomes near 100% profit for the airline/frequent flyer program.

Even if you do use the miles, the cost to the airline is generally far less than what they sell the points/miles for.

Whether or not the airline can "sell" your personal information is something that should be contained within the terms and conditions you agree to when signing up for the program, and would vary depending on the company and country(s) involved.

You need to read the privacy policy and terms and conditions of your specific airline's program as they should detail if they share any information and with whom.

Keep in mind some information sharing is mandated by the regulator or the country (such as API); this is simply a cost of traveling.

The main source of revenue is selling points to other providers. It is such a huge business that there are brokerage companies out there that bid on these points and agreements for their clients; and there are aggregators that will "buy" points for their clients and their platform.

The reward of a loyalty program (especially if you travel frequently) often outweighs the cost of privacy. The airline already has a lot of information on you - generally they have information on some government issued id (if you travel internationally, the also have your passport details) along with usually some form of payment instrument.