Because cops are human, and most people answer questions when cops ask them questions. Refusing to answer questions cannot be held against you in court, but it certainly often is in the minds of humans. And when a cop has "evidence" against you that they cannot use in court, that's when it seems likely they'll manufacture some evidence that is usable.

Cops being human is also exactly why the lawyer and detective in the video is exactly why never talk to cops.

Real lawyer opinion > armchair lawyer opinion.