Argument for a two point conversion: It mathematically and undeniably increases your odds of winning. If you can't see that after eight pages (pocha has done a good job of explaining it), then your brain is simply not capable of grasping what should be pretty basic statistical probabilities. And that's okay; if everyone were good at math and reasoning, the world would be a much less interesting place.
Arguments against a two point conversion:
(1) You "extend the game" by kicking an extra point. No, you don't. A game is 60 minutes. Down 15 with a few minutes remaining, YOU WILL NEED A TWO POINT CONVERSION AT SOME POINT, NO MATTER WHAT, and your odds of converting do not change based on when you elect to go for two. If you kick the extra point with 2:05 left, there's 2:05 left. If you go for two with 2:05 left, there's 2:05 left. If you kick the extra point with 0 left, there's 0 left. If you go for two with 0 left, there's 0 left. Pocha played out the scenarios for you. It doesn't matter when you go for two if you're successful. However, if you're unsuccessful, you would rather be unsuccessful with two to three minutes left than with no time left.
(2) "90% of coaches go for the extra point." Show me proof. And either way, I don't care. That's not a logical argument. Give me an actual reason, other than "but, but, but, all the cool kids are doing it!!!" Explain to me why the cool kids are doing it. I'll wait. (Edit: I thought about this some more last night, because in my personal experience, coaches often do kick the extra point, despite it giving their team a statistical lower chance of winning. That's never made sense to me. Then I realized that this thread is the reason why coaches kick the extra point: they realize that (1) going for two only increases their chances of winning by a very small percent [maybe 1/4%?], and (2) if they go for two on the first possession but fail, a surprisingly large number of uninformed fans will blame the coach, at least in part, for the loss. The safe bet for a coach looking to avoid fan criticism is to kick the extra point and therefore turn the focus back to the team for the last minutes of the game. If the team doesn't convert the two point conversion with two seconds left, fans will leave somewhat content knowing that at least the team came close. In other words, it's actually a very cowardly but understandable move for coaches to kick the extra point: it's cowardly because it decreases their team's chances of winning, but it's understandable because it avoids irrational fan criticism.).
(3) "Momentum is important." How much momentum will we have when we kick the extra point, recover the onside kick, drive the field, score, then FAIL to convert the two point conversion with 2 seconds remaining? The answer is ZERO. We will have ZERO momentum at that point, because we will have LOST THE FU**ING GAME as a result of our coach failing to put is in a position where our offense could manage the clock based on the need for two scores. The fans will shuffle out completely momentumless. Alternatively, what if we go for two early, fail, recover the onside kick, then Wadley busts a screen for a touchdown on the first play? Now we're looking at a two point game with maybe 1:15 to play. That's a boatload of momentum at that point, and it's the only scenario where we can potentially recover from failing to convert a REQUIRED two point conversion.
(4) "You've obviously never played football." You're obviously a fu**ing idiot.
