'e didn't so much fly as plummet.
Regarding gliding:
Anon Coward above is partially correct in that they did not have the altitude to play with in this case, however the idea that airliners glide "like a brick" is incorrect. In fact most jets, including airliners have excellent glide ratios for non-soaring aircraft, typically much better than most light airplanes. The A320 has a glide ratio of about 17:1. In other words at best glide speed it moves forward 17 feet for every foot it descends. That's more than double the glide ratio of a Cessna 172 at 8:1. The big difference here is that the A320 is moving a LOT faster to achieve that glide, and so it needs more room to land.
Teterboro may have been close enough to glide to, but it is a relatively small airport (read shorter runways) closely surrounded by dense residential areas, with some very tall transmission towers just to the south of the airport. What's more, its runways are not aligned with the direct flight path to the airport, so they would have had to maneuver, thus using up more altitude. Had they chosen KTEB they would have had to maneuver to align with the runway, visually locate and dodge those towers and then put the plane down right on the numbers to make it work. In the Hudson they had all of the space (in all three dimensions) that they might choose, as well as rescue services close enough to be useful. While it carried its own risks, landing in the river was a much safer choice than trying for Teterboro.