The main "practical" reason is your personal security. Despite anonymization, the kind of data collected by these companies is generally enough to identify you easily. A bad actor at that company could do you quite a bit of harm. So could a politically hostile government, if it demands the company hand its data over.
And with the exception of HIPAA-controlled medical data in the USA, the company that collected the data is free to do anything it wants. It can resell the data, or store it in 10 places and never delete it. This means the window of risk for your data being compromised and used against you extends far into the future.
There is also the general belief that, if any of this data collection and tracking we're done off-line it would be considered terrifyingly creepy.
So even if you have "nothing to hide", as many of us don't, it's not necessarily about protecting what you have right now. It's basically saying that people have a right to some amount of basic privacy, if only to protect their individual personal freedoms and security. Therefore we should take a principled stand against unmanaged black-box data collection at all times, in the same way that people in the USA try to defend their rights to free speech and press even if it does not necessarily affect them in daily life.
So it's about protecting your personal security now and into the future, as well as taking a principled stand on something that should be considered an individual right.
Edit: in this particular case they are interested in knowing how and why you saw some search results or some advertisement as a result of whatever algorithms are being run on your data. This is probably in response to increasing news coverage of people being unduly influenced by various search and advertising algorithms out there on the Internet. Personally I don't know if I care specifically about the algorithms, I just care what data has been collected, where it is being kept, and how I can have it deleted or not have it be kept in the first place.
And with the exception of HIPAA-controlled medical data in the USA, the company that collected the data is free to do anything it wants. It can resell the data, or store it in 10 places and never delete it. This means the window of risk for your data being compromised and used against you extends far into the future.
There is also the general belief that, if any of this data collection and tracking we're done off-line it would be considered terrifyingly creepy.
So even if you have "nothing to hide", as many of us don't, it's not necessarily about protecting what you have right now. It's basically saying that people have a right to some amount of basic privacy, if only to protect their individual personal freedoms and security. Therefore we should take a principled stand against unmanaged black-box data collection at all times, in the same way that people in the USA try to defend their rights to free speech and press even if it does not necessarily affect them in daily life.
So it's about protecting your personal security now and into the future, as well as taking a principled stand on something that should be considered an individual right.
Edit: in this particular case they are interested in knowing how and why you saw some search results or some advertisement as a result of whatever algorithms are being run on your data. This is probably in response to increasing news coverage of people being unduly influenced by various search and advertising algorithms out there on the Internet. Personally I don't know if I care specifically about the algorithms, I just care what data has been collected, where it is being kept, and how I can have it deleted or not have it be kept in the first place.