Trivia: The spears shown in the lab are from Predator 2 and Alien vs Predator.
Trivia: When Rory is walking down the street wearing the Predator mask, there is a bright red/orange alien walking toward him. This is a nod to the original Predator costume that looked like a big bug, the red/orange color was used to film the stealth camouflage scenes. The bug suit was scrapped after a few test shots proved how silly it looked. Jean-Claude Van Damme was in the original costume, but he was let go when the costume was scrapped. (00:45:20)
Trivia: Gary Busey, who played Peter Keyes in Predator 2, is the father of Jake Busey, who plays a doctor in this film.
Trivia: Spoilers. Originally, Shane Black wanted Arnold Schwarzenegger to make a cameo in the end - he would have been the "Predator Killer" that rises from the device right before the credits. When he decided not to return, the "Predator Killer" was changed into a highly advanced suit of armor.
Trivia: The line on the poster "You'll never see him coming" was used by The Mandarin from Iron Man 3, also directed by Shane Black.
Answer: The Predator had landed in the middle of a group of hostile Earth soldiers, who it judged would likely have just shot it immediately. It would have defended itself. And there's also the fact that it could just be for fun because, hey, old habits die hard.