First, governments already have all the data they want from you. There's no way around that. Second, the more information you have on the internet, the easier it is for someone to take your identity. Look up security breaches and hacks and it will become very obvious since many places put your personal info on the web while guaranteeing your info is safe. Third, there are databases that aren't illegal that store your personal info that people can research to track you down. And it's not originally meant for unscrupulous reasons. These databases were first meant to replace phone books which would post your contact number and address, but those have since been used for shady business. For example, if you get a lot of spam calls, that means you are on an internet database somewhere.

Another example of why it's important is a personal experience. I was deployed, and my parents started getting messages from random people asking for my exact location and what operation I was involved in. They claimed they served with me and they wanted a way to send me mail. They refused and then started getting threats of having my niece and sister taken. When I found out, I got NCIS and the FBI involved and not long after the investigations started, there were no more messages.

Another example I can give to you is what started my perma ban on reddit. I saw the story of a man in Wyoming who accidentally ran a wolf over (the wolf was very injures). So instead of putting it out of it's misery or calling animal services, he paraded the hurt animal around a bar for a few hours before taking it out back and putting it down. I found his phone number on aforementioned databases and posted it on reddit.

The moral of the story is that you are available and findable if you do not take proper steps