The Seahawks didn't say "they want to kick" or "they want to receive". They deferred giving the Patriots the offer to kick or receive and the Pats chose to receive (notice how the Ref turns towards the Patriots and asks them if they want the ball). The Seahawks then got to decide which goal to defend.
I don't know why the Pats did not choose to kick but, apparently, if they had done so they would have kicked at the start of the second half as well (from what I have read somewhere).
I actually remember reading about a college game recently where a team deferred and the other team chose to kick (I think this is how it went down). The team that chose to kick also had to kick in the second half as well so they lost both possessions.
I'm just really confused on this whole coin toss/deferring thing. Hopefully someone here has more knowledge and can better explain and possibly correct anything I've said that is wrong.
EDIT: Here is a small article on the College game where the team had to kick in both the first and second halfs....
http://deadspin.com/texas-botched-the-coin-toss-has-to-kick-off-to-ucla-bo-1634479396