
With some movies, this option is absolutely absurd. 2001: A Space Odyssey, for instance. The first several minutes contain an overture, meaning it's a black screen with music by György Ligeti, music that is practically inaudible for the first minute. And it's not just 2001 where this option fails. Frankly, it fails on most movies. Even modern movies that don't like a long opening credit sequence without some form of action don't get the story rolling until well after the two minute mark. A better option might be to

One of the pros of watching the ending is that most movies don't have twists that occur within the last two minutes, often leaving time for the final denouement after the twist. For instance, in a "big twist" movie from the nineties, The Shawshank Redemption, the last two minutes don't reveal the twist but instead Morgan Freeman walking along a wall, extracting a box full of money and meeting Tim Robbins on the beach. To someone who'd never seen it, this might elicit a "What the... What's that all about? How'd they get to that ending I wonder?" As such, think of the curiosity struck by seeing the last two minutes of some very famous movies had you never seen them before.
"Hey, the catatonic guy in the bed just got smothered to death by a big guy who then threw a sink through the window. The fuck?"
"Hey, look, it's kind of like a Nazi rally and those two guys are getting medals while a couple of robots and a big dog-man look on. Wow, what the hell connects those dots?"
"Check it out, there's this dock worker, all bloodied and beaten, walking towards a ship and a bunch of guys are following him. Huh?"
"Someone's slaughtering a water buffalo or cow or something while another guy whacks some big bald guy. Isn't this about Vietnam?! How the hell'd we get here?"
"Cool, the guy in the French hat totally covered for the guy in the trench coat and now they're walking off into the fog talking about their friendship. Wonder where that came from."
Of course, while it may make watching the whole movie enticing in some cases, on the whole, it's probably too risky watching the last two minutes. I mean, "Rosebud," "Forget it, Jake, it's Chinatown," "Frankly, my dear, I don't give a damn," and "It's the stuff dreams are made of" kind of spoil the climax in a major way and happen right at the end.
Which leaves us with two minutes selected from a random point in the movie. This is my personal choice and here's my completely unscientific reason why: How many times have you been flipping through the channels and seen a movie starting, then decided to keep on flipping to see what else is on while that movie started? And you did this because you knew the first couple of minutes didn't matter that much for your casual late night, channel-flipping purposes. You wanted to see what else was on, right? Now, how many times have you been flipping through the channels and come across a scene from a movie, at some random point in said movie, and been transfixed? Exactly.
Online rental companies, drop the first two minutes preview. It's crap. Give me two minutes at random and I'll given you purchases that are specific, and I'll do it all in under sixty seconds.