The reasons for the move are mainly that we get a bit more say in electing the President. You could also make the argument that since we're more representative of America than, say, Iowa or New Hampshire, two states that pretty much describe the phrase "white bred," it'll be more representative of what the country really wants.
The reasons against is that we're the 800 pound gorilla and our presence early in the primaries' could throw the whole darn thing out of whack. Something that could actually be a good thing. Last time we moved up our primary date, a bunch of smaller states moved there's up to get in ahead of us. Already, the DNC is threatening to take away some of our delegates to the convention (oh noes!) if we do the move because they're afraid of the effect we'll have. Another reason against it is that it'll cost us much more money to prepare for another election. The plan is to have the primary in February but still have a bunch of legislative elections in June. That's three elections in a year, four for those places that don't have ranked voting and have to have run-offs. Ironically, this is something that legislators like because they're hoping to also put a rule changing term-limit rules on the February ballot so they can have enough time to put them up for reelection by June.
Which is why legislators like the idea. And Arnie, who likes the idea too, is thinking it might be a good time to throw a redistricting measure up there too because all the legislators are so into the idea of changing term limits that they'll support anything. It's a win-win!