People can get details of how you spend your money. Using a public address as a public person let's everyone see what you are doing with your money.
That's not exactly true.
You can see that bitcoin went to another address, but addresses are mostly unknown and anonymous.
If you are paranoid, you can have a public through out address where you can receive money and them just "clean" those bitcoins in a bitcoin mixer, for example.
Bitcoin transaction and history should be private and unidentified that's why people are using cryptocurrency because of its confidentiality. Don't be paranoid and be comfortable with your bitcoin wallet as it is probably safe if you try to monitor it. Sometimes knowing the addresses will let you know if you successfully transfer your money from one another or if the transaction is a success. But in public, you should not let other people see it as this will be the way for those hackers to get your information, they will take advantage of the chance where they will scam your wallet. Always be careful on using cryptocurrencies, privacy is important in all of the aspects in our life so we should always manage and keep it no matter what.