It's unlikely to "break" it.... although in time, repeated use could wear down some of the port, which would could result in a device not being fully seated correctly in the port. That's all 'in theory' though. In practice, years & years of frequent use of a USB port isn't going to break it - and charging would simply be one "use" of the port.
What could happen (although not exclusive to charging), would be a defective device at the other end of the cable. If the device is sending voltage back down to the USB port of a laptop etc, then there are protections built in to shut down the port (to prevent incoming voltage). That could give the perception of it being "broken", when it's actually only shut down to protect itself.