What we are more interested in during meditation is becoming aware of these thoughts and understand through observation, that your thoughts are not you. They have a life of their own, and you can only accept what they suggest or behave differently. You can’t control your thoughts, but you do control your reactions, and when you learn to dissociate from the thoughts, they suddenly lose their power over you.
With time, as you observe your thoughts, you start noticing that thoughts appear and disappear. Think of your brain as an airport lounge and thoughts as passengers in transit. They arrive at the airport, spend some time there, but eventually onboard a plane and leave to another destination. Your thoughts are transient, they only spend limited time in the brain.