That's not what your parent said: they said when there's any really bad news about a company who advertises on Twitter, that company doesn't want its ads shown right next to that news.

I don't think it's that necessarily; instead, you could pause Southwest advertisements until the next news cycle for example, or look for keywords in tweets and avoid showing SW ads near such tweets (e.g. normally you want a SW ad near tweets with "airport" but for the next 5 days you want the opposite approach)

No, I don’t think you read that correctly. The thing that’s removed is the advertisement, not the news. Eg if I tweeted “HackerNews sucks”, they would not want to pay to advertise on or near my tweet. They would rather advertise in a more neutral or positive space. Someone else could fill that advertising slot (eg. McDonald’s).

I mean you are very clearly not reading it right since the commenter's comment had nothing to do with suppressing news and only had to do with where paid advertisements are placed.

You have it the wrong way around. The advertiser will ask for the ads to be suppressed or removed from negative contexts, because that's part of the service they pay for.