What do you do with clouds that you dislike?
Trying to suppress a thought will keep it alive because you’re spending time and energy on it. Trying to ignore it wouldn’t be that different. You’re still trying to get rid of it and in an attempt to ignore it, you might avoid situations that could trigger it, which is putting the thought in charge of your life.
If somebody asked you to try to suppress a cloud in the sky, it would be very difficult and you would have to spend lots of time and energy figuring out a way to get to the cloud and get rid of it and you’d constantly be checking on it or trying not to look at it. Everything would be happening in reaction to the cloud. So it can help to treat thoughts the same way most people treat clouds: they don’t actively spend energy on surpressing them or trying to ignore them. They also don’t spend energy focusing on them or trying to do anything with them. Why bother with them at all?
When somebody is trying to figure out how to suppress or ignore a thought, it’s usually the case that the compulsion they’re actually struggling with is judgment. If you label that thought as bad, horrible, unwanted, etc, that’s going to create anxiety because you’re having a “bad” thought that you don’t want to have. You might be judging yourself for having that thought, afraid of what it means, afraid that people will find out you’re having that thought–and then you really want to get rid of it. So it can help to shift the focus to accepting thoughts, rather than trying to suppress or ignore “bad” thoughts. What’s the use of judging the clouds in the first place? You can put the clouds in the sky in charge of your life and your emotions, but is that going to be useful to you?
As long as you engage in that compulsion to judge your thoughts, you’ll keep putting yourself in the situation of trying to escape the unescapable.