I will step by step it.
1: watch news - baby died in hot car, car crash killed family of 6, Trump said this or that, crime wave hits some city you don't live in, natural disaster in some country
2: be scared/fearful that something will happen to you.
3: worry about these things that you cannot control
4: see a post that says "I was scared but then I didn't read news and it was better for me" think that fits you and is interesting so you read it and like what it says. (instead of a post that states "Newscasters are owned by the rothchilds and they bow down to them and show you only what the elites of the world want you to see in a way they want you to see it and pizzagate is the truth and you are a goddamn moron if you believe a word that the mainstream media spew from their mouths" again, this is just for example and doesn't mean I believe in that alternate title but I hope you can see the more gentle nudging in how I write to potentially awaken people to alternatives in life)
5: try watching no news
6: see that you have less worries in life and more time
7: use time to broaden your mind/skills
8: decide to see why news is like it is
9: see some form of conclusions I wrote about in my "don't watch the news post"
10: decide there is some nugget of wisdom in there and you find your own meaning towards it
11: use this rational to look deeper into other things you took for granted
12: see that everyone has an agenda - for control, for money, for power, for fame, for anything
13: live outside the cave

Ok, this is one possible example of one possible path. Note that you did not stop watching the news because you were scared in the moment - you put aside the emotion when you made the decision to not watch the news. You listed pros and cons - logically. That does not mean that emotions do not fall under one side or the other or both, it means that you do not use your current emotional state to make the decision. They can be but one pro and/or con in a list of positives and negatives.