President Trump regularly uses his Twitter account to personally attack and demean others. He consistently violates Twitter policies, but he's held to a different standard because of his title. Some say enough is enough—it's time to ban Trump from the platform.
The president's latest tweets are not a one-off occurrence. Trump regularly does this—he gave fuel to a conspiracy theory about Seth Rich, which tormented Rich's family. It's not a harmless thing that Trump does.
However, Trump's supporters enjoy his Tweets and think that he is expertly trolling the liberal media. In their eyes, Trump is playing the "media elite" and the "blue-check" class. They revel in the hand-wringing and see no harm in the president giving air to conspiracy theories and using his platform to attack his opponents. Besides, he's the president. He has a huge platform without Twitter.
Twitter's position is that since Trump is the president, his tweets should be left up because there is a clear public interest in them. As president, what Trump chooses to post is relevant regardless of anyone's personal opinion on him, according to Twitter.
Here is the specific criteria Twitter has laid out for when they would take down a world leader's tweet.
Promotion of terrorism;
Clear and direct threats of violence against an individual (context matters: as noted above, direct interactions with fellow public figures and/or commentary on political and foreign policy issues would likely not result in enforcement);
Posting private information, such as a home address or non-public personal phone number;
Posting or sharing intimate photos or videos of someone that were produced or distributed without their consent;
Engaging in behaviors relating to child sexual exploitation; and