Yes, I was told ahead of time not to wrap anything before getting on the plane, so I didn’t, but I’m still puzzled by this. What difference does it make if they’re wrapped or not? Can’t the scanners see through wrapping paper? I would understand if the packages weren’t sent through the baggage scanner, but I don’t understand why a wrapped gift in my suitcase that’s being scanned anyway has to be unwrapped?
Haven’t flown lately, huh? 
Here’s the deal. While you’re waiting in line to board the plane, you’re going to have about a 1:20 chance of getting pulled aside. You will be made to spread 'em and then balance on one foot and then the other while one Highly Trained Security Person goes over you with a metal detector wand, pausing occasionally to bang the wand against the heel of his/her hand and complain to the other Highly Trained Security Person that it’s a piece of junk. Meanwhile, the other Highly Trained Security Person will paw through the underwear in your carry-ons, in most cases in plain view of the rest of the passengers in the terminal. If this highly trained security person finds any wrapped packages in your bags, (s)he will unwrap them.
Also, your checked luggage may be hand searched. The good news: everyone in the terminal won’t be able to see it. The bad news: neither will you.
From United Airlines :
Wrapped Gifts - Those traveling with gifts as carry-on or checked baggage should not wrap them. All items are subject to searches including wrapped gifts.
They don’t say you can’t wrap gifts. They are just warning you that if a wrapped gift looks suspicious on the X-Ray, it will be unwrapped and inspected, regardless of how long it took to wrap it just the way you wanted it. We flew from Phoenix to Denver on Christmas Day, and saw several wrapped gifts that didn’t look like they had been opened. Probaly safe looking stuff like sweaters and teddy bears.
This isn’t a new request either - airlines have been asking this for years. Like SuperNelson said, it’s just a warning that they might have to undo all your work if scanning brings up something suspicious.
:smack: Didn’t even think of getting pulled aside and searched. Thanks for the replies, guys.
I’m not sure why I thought this was a recent phenomenon.