Mostly a fallacy, as many people assume this at first.
Imagine yourself being on the bus or the train. Other people are surrounding you. Would you say out loud what you are typing into your smartphone? No? Then, why would you trust any app or service on your device to not mess with what you are inputting?
Why privacy matters
Types of privacy issues
Even benevolent services, not selling or sharing your data might suffer from these issues: Data leaks