What people don't seem to understand this is that it wasn't actually about the time on the clock, but it was about the personnel package.
The Seahawks were in their two minute drive package. [Note: this part is inaccurate, per Pete Carroll as quoted below. Rather, according to Coach Carroll, they put three receivers out to spread the field to make the run easier, assuming that the Patriots would have to defend the catch. Coach Belichick called his bluff by sending out the run defense unit anyway, essentially daring the Seahawks to pass.] They had three receivers on the field. It's not the best package for the goal line.
They assumed the Pats were going to call a timeout to stop the clock, but Bill liked his personnel matchup better than calling the timeout and letting Seattle bring in its heavy lineup. [Furthermore, according to this article quoting Matt Patricia, the Patriots actually wanted this matchup on the field. They were baiting the pass.]
Seattle didn't want to use their timeout to change the personnel, because they though they could do one pass play, stop the clock, and change out the personnel...and save the timeout for after the Lynch run on 3rd down.
It all makes a ton of sense. I get the playcall from both sides. Great coaching, and one team executed at the right time.
and his explanation is backed up by Pete Carroll's explanation of his own decision:
Under questioning by sports reporters, Carroll explained: Heres the deal. We sent our guys on the field wide receivers on the field to spread them out. They ran on their goal line (package), they got all their big guys out there.
At that moment, I didnt want to waste a run play against their goal line guys, throw the ball and come back on 3rd or 4th (down) where we could match up. So it was really a clear thought
but it didnt work out right. We throw the ball
and they make a big play.
It was just because of the match-ups, he repeated. Theyve got extra guys on the line of scrimmage so we didnt want to waste a run play.