Presumably if Trump were to stop tweeting and move to a different social media platform (e.g., Instagram), Twitter's value would decrease significantly (source estimating Trump's value to Twitter).
Would it be illegal for him to short Twitter stock and then make this switch? If so, why?
The President wouldn't be in breach of Insider Trading Laws (Section 10b of the Securities Exchange Act) since he has no information resulting from a position of trust within Twitter (or as a trusted provider of services) and no ability to depress their stocks through intentionally fraudulent practices.
[O]ne who fails to disclose material information prior to the consummation of a transaction commits fraud only when he is under a duty to do so. And the duty to disclose arises when one party has information “that the other [party] is entitled to know because of a fiduciary or other similar relation of trust and confidence between them.”
The key word here is "insider". The President is not an insider, he's merely the user of a service. He certainly has material information, but not gleaned from a position of confidence or trust.
anyone in possession of material inside information must either disclose it to the investing public, or, if he is disabled from disclosing it in order to protect a corporate confidence, or he chooses not to do so, must abstain from trading in or recommending the securities concerned while such inside information remains undisclosed.
That being said, it's arguable (and I'm reasonably sure his political opponents would argue it until the cows come home) that his shorting their shares would be a material violation of the STOCK Act, specifically section 6 which requires the President to have disclosed his holdings of shorted stock to the public.
It's also pretty arguable that his popularity on Twitter is a direct result of his office as President, and hence making money by publicly and messily leaving their service will result in a breach of accepted ethical standards and potential impeachment even if no specific law has been broken.
Potentially applicable would be SEC rules 10b5-1 and 10b5-2, which would prevent certain individuals from buying or selling securities, if you have material private information (such as "I plan to give up on them, which will probably cause a dip in value"). These rules don't prohibit everyone from acting on the basis of what they know: there has to exist a fiduciary duty or other relationship of trust and confidence. As far as we know, he has no such relationship to Twitter. So he has no more obligation to patronize that service that you have to shop at Walmart, or company A has to renew a contract for goods or services with company B. Boycotts are not illegal in the US, and have been used in the past (and continue to be used) for various political purposes. The terms of service for use of Twitter do not in any way bind a user to continue using that service in perpetuity. The First Amendment also allows one to choose what viewpoints they will express, and where they will be expressed.
