For something like a corporate jet, allowing tracking could give away (or at least suggest) company secrets that could affect the stock prices or financial performance of a company.
To use an extreme (completely fictitious) example, say that the Target store chain had a corporate jet. And somebody noticed that that jet was suddenly making weekly flights to XNA airport, in Bentonville, Arkansas… Somebody noticing that might infer that Target and WalMart were working together on something at the Executive level - Merger? Acquisition? Joint Venture? Whatever it happened to be, the news might leak before it was ready.
Likewise, planes owned/leased by celebrities might be hidden to thwart paparazzi, or just to reduce crowds of fans everywhere. If you see that John Travolta’s plane has a flight plan filed for a small regional airport like FAT, it’s not going to be hard to figure out where to find him.
So there could be any number of non-nefarious reasons for not wanting your plane tracked.
Aren’t there some sites like ADS-B Exchange that don’t sign up to keeping private the tracking of planes? In other words they allow tracking of any and all flights.
The FAA has privacy programs, LADD and PIA, to delink ADS-B from all personaly identifiable information. This privacy protection is only good for domestic flights. All international flights must use real identifers. Aircraft enrolled in these privacy programs can still be tracked, but there is no way to identify the actual aircraft.
Edit to add: If you’re out in public, I don’t think you have any right to expect privacy. Example, you can take a picture of anyone in public. They can’t stop you. So I don’t completely agree with what obj said about GPS tracking of cars. If you want complete privacy, stay in your house (with your internet disconnected).
The FAA assigns private (fake) ID codes to use in the transponder (ADS-B). One can track the fake codes, but there is no way to identify the owner info.