Why did they conclude that it should only be 4 instead of 8/16?
Interesting question. The BCS has been plagueing college football for quite some time and the NCAA, among many others have finally have brought up the new College Football Playoff system to try and resolve the former's well documented criticisms. There really is no direct answer to your question, it's just as Charles Sterger (the President of the CFP system) says:
Reading into his quote, he's clearly indicating it could very well have been a number higher than four (no less, of course). But I'd like to say they went with four for two simple reasons: 1. It will give more teams the opportunity to compete for the National Championship, and, 2. Limiting it to four will still ensure only elite teams are going to be playing for a chance in the game. Undoubtedly they have looked at past seasons and must have seen anything above 4 to be the cutoff for these "elite" teams, to become "very good" teams.
The Wiki on the CFP is actually a pretty good read. There will be 13 people apart of the "Selection Committee". Ranging from Archie Manning to Condoleezza Rice to a former Air Force Academy superintendent. All 13 are well respected, proven to give as unbiased of selections as possible for the four teams that will play in the playoff for the championship. Their seedings [1,2,3,4] will follow the general playoff pattern in which 1 plays 4, and 2 plays 3. The schedule for the Bowls the semifinals will be played in is already posted on the Wiki as well.