They are not true and they are not 'you'. And even if they sometimes are accurate, they're not permanent or true in all cases. But mostly, they're just plain false, or hyperbole, or misunderstandings, or projections, or just plain random. They are just mind objects that pop in and out of your awareness, based on conditioning. Your mind will keep on supplying your awareness with the kinds of thoughts that it generally focuses on.
So here's how you do it: don't try and suppress your thoughts or make them go away. But when one pops into your head, simply note objectively that a thought popped up, categorise it as negative, positive, or neutral, and and allow it to go away. If it's got some utility to it, like "I need to feed the dog", follow it through. But don't get dragged into believing it, especially if its just negative and unhelpful.
Humouring your internal negative dialog is like arguing with crazy strangers on the internet. It's pointless and a waste of time. You don't have to take on and identify with their statements and opinions.
Here's a talk(it's from a Buddhist monk) on this very issue that might help you, if you're open to it. http://www.amaravati.org/audio/negative-mind/