"Even if he isn't questioned under oath, Trump could still open himself to charges if he lies to Mueller's team, since lying to the FBI is also a crime."

Trump also has a long history of not listening to his lawyers when it comes to lawsuits and his preparation of them. Even if he isn't questioned under oath, Trump could still open himself to charges if he lies to Mueller's team, since lying to the FBI is also a crime.

Trump would likely make the obstruction case for Mueller if he would agree to be questioned under oath. The obstruction of justice area of inquiry illustrates the difficulty Trump would face if he agrees to questioning by Mueller. Mueller would have to establish that Trump acted with "corrupt intent" in trying to derail the Russian probe. This is an extraordinarily high burden.

He'd ask why Trump instructed his White House counsel to urge his attorney general not to recuse himself and raged at Jeff Sessions' failure to protect Trump from the probe. No answer Trump gives will help end the probe. Rather, it will make Mueller's case.

Mueller earned his reputation for being an extraordinarily effective prosecutor. He worked for 12 years in the U.S.'s Attorney office and has investigated and prosecuted crimes ranging from major financial fraud to public corruption cases. Trump and his lawyers simply don't know what information Mueller has, and who has flipped and provided information to him.

Optically, staying quiet would give the president's critics a field day at his expense. Refusing an interview with Mueller could have steep political costs and be seen as an implicit admission of guilt by the president. But misleading the special counsel will likely end his presidency.

There is truly nothing to gain for the president by cooperating with Mueller but there is an impeachment to lose. Only four sitting presidents have been deposed in our country's history. One of those presidents, Bill Clinton, was impeached for lies he told during that deposition. If Trump agrees to be questioned by Mueller, he will likely end up in the same position.

Commentary by Andrew Stoltmann, a Chicago-based attorney who has handled a broad range of both criminal and civil matters in federal and state court. Stoltmann primarily represents defrauded investors in lawsuits across the country against companies like Merrill Lynch, Wells Fargo, and UBS. Stoltmann is an adjunct securities law professor at Northwestern's School of Law in Chicago. Follow him on Twitter @stoltmann1971.

For more insight from CNBC contributors, follow @CNBCopinion on Twitter.

Correction: An earlier version of this article said sitting presidents can't be subpoenaed or forced to answer special counsel inquiries. It is unclear whether that is the case and it could become an issue for the Supreme Court to decide.