Watch the James Duane video; he does a better job of explaining it than I. But I'll try to give some reasons:

1. Officer asks a question; passenger gives a response. A little while later in the conversation, officer acts the exact same question --- except this time, the passenger gives a slightly different response. The officer can jump on the contradiction as a willful lie, and charge the passenger with obstruction of justice.

2. In the course of the discussion about the supposed "crime", evidence of other "crimes" could be inadvertently revealed. Silly hypothetical: if the passenger says that he left his hotel an hour ago to drive to the airport, and the hotel is 100 miles from the airport, the passenger has just inadvertently confessed to speeding. Now, speeding may not be much of a crime ... but now the officer has probable cause to push further, and more problems result.

3. Intent to commit a crime is irrelevant ... ignorance of the law is no excuse, right? And unless you're an expert on the thousands of laws that apply to you as a citizen in a particular city, county, and state, there's no way for you to know that "you haven't committed a crime" at any given moment.

Keep in mind that while TSA is supposed to be focused on the security of air travel, its employees are required by TSA policy to report any potential violation of any law, whether or not it's related to TSA's mission. So ... remaining silent (or, at least, non-responsive) isn't as irrational as it might seem.