But for Dick Costolo , the former Twitter CEO who ran the micro-blogging site from 2010 to 2015, including taking it public in 2013: "I completely, 100 percent agree with [Twitter's] decision to leave Donald Trump's account up," Costolo tells CNBC Make It .

Trump doesn't seem to filter what he says on the platform, often posting what many say are dangerous tweets. So much so that there have been calls to ban the President from the platform.

Since Twitter was founded in 2006, the popularity of social media has exploded, but that doesn't explain the radical difference in tweeting between Barack Obama and the current president.

No President of the United States has ever tweeted like Donald Trump .

"He is the President of the United States. People should see what he has to say. They should see what he thinks."

Several posts in particular have brought the Trump Twitter debate into the limelight. The President's tweet in September calling North Korea's leader Kim Jong Un the "little rocket man" raised considerable angst when North Korea said the tweet amounted to a declaration of war.

Just heard Foreign Minister of North Korea speak at U.N. If he echoes thoughts of Little Rocket Man, they won't be around much longer!

Graphic violence — including "any form of gory media related to death, serious injury, violence" — is prohibited from Twitter, as are threats of violence and terrorism, according to the current Twitter rules.

Twitter left the tweet up, though that decision ignited a tense conversation over whether Twitter was appropriately adjudicating its authority as a publishing platform.

At first, Twitter would not comment on w hether the tweet denied its terms of service, but eventually said it did not take the tweet down because it is newsworthy.

THREAD: Some of you have been asking why we haven't taken down the Tweet mentioned here:

In early January, Trump again tweeted about North Korea, comparing the size of his own "nuclear button" to that of Kim Jon-Un's.

North Korean Leader Kim Jong Un just stated that the "Nuclear Button is on his desk at all times." Will someone from his depleted and food starved regime please inform him that I too have a Nuclear Button, but it is a much bigger & more powerful one than his, and my Button works!

This time, Twitter said that Trump's tweet had not broken its existing terms of service, and later released this statement: "Blocking a world leader from Twitter or removing their controversial Tweets would hide important information people should be able to see and debate. It would also not silence that leader, but it would certainly hamper necessary discussion around their words and actions."

Costolo tells Make It he also believes there is value in the transparency Twitter provides.

"You can go back and see what people have said over time and understand whether they're contradicting that something they said two years ago or one month ago," says Costolo. "I think that's a benefit to the world." (Though it's possible for users to delete tweets.)

For example, in 2015 and 2016, Trump tweeted about his respect for women.

Hillary, when you complain about "a penchant for sexism," who are you referring to. I have great respect for women. BE CAREFUL!

The media is so after me on women Wow, this is a tough business. Nobody has more respect for women than Donald Trump!

Then in October 2016, a recording was released of a 2005 conversation in which Trump said, "I'm automatically attracted to beautiful women — I just start kissing them, it's like a magnet. Just kiss. I don't even wait. And when you're a star, they let you do it. You can do anything … Grab 'em by the pussy."

And a January Wall Street Journal expose unveiled an affair Trump had with the porn star Stephanie Clifford ("Stormy Daniels"). The tryst reportedly happened in July 2006, a year after Trump married Melania.

But there are limits, Costolo admits. Hinting at the controversy regarding Trump retweeting anti-Islamic material posted by far right Britian First leader Jayda Fransen in November, Costolo says, "Do I think that when people do things like a retweet of a violent video that's in violation of the terms of service — that that video should be removed? Yes. I also think that that that you should be consistent about about things like that."

In December, those tweets were removed as part of a new policy Twitter rolled out "to reduce hateful and abusive content."

Many are not happy with Twitter's decisions. More than 14,000 signatories have endorsed an effort to remove Trump from Twitter on Change.org, for example. Others have criticized the platform for what they call its lackadaisical and self-protective policy updates.

"Ultimately it is up to the officers of Twitter whether Trump is allowed to continue abusing people, institutions, corporations, and the planet with your powerful technology. To be blunt, Twitter is becoming with each day more complicit in everything Trump does and will do," the Change.org petition says.

"People are increasingly demanding an explanation for Twitter's failure to enforce its rules, and the justification offered so far — that his tweets are newsworthy — is nothing more than greed. Ask yourselves, do you want to be remembered as the corporation that helped start World War III? We hope you make the right decision, and soon."

Further, a group of protestors projected a number of messages onto the San Francisco Twitter headquarters in early January criticizing the platform's decisions to leave Trump's account active. Senior tech reporter at Buzzfeed Alex Kantrowitz shared a number of those pictures, of course, on Twitter.

Protestors now standing outside of Twitter HQ

Here's what they're projecting on Twitter HQ tonight: A Tweet Starts WWIII?

And: History Is Watching

See also:

Why Twitter won't take down Donald Trump's tweet which North Korea called a 'declaration of war'

Twitter shut down white nationalist accounts, including one that Trump retweeted

Trump retweets far-right British group's shocking anti-Muslim videos