The way I see it, the Predator isn't trying to take down his opponent with him. Instead, he, being the honor-bound hunter/sportsman that he is, feels that failure is not an option and if his prey lives, he is not worthy of living. Imagine the shame you'd get in such a culture if you set your eyes on a target and got your ass handed to you, despite all of your technology.
I know this isn't the best source, but the game "Predator: Concrete Jungle" shed a little light on this. At the beginning of the story, our Predator is on the verge of death, making its escape from angry mobsters after killing their boss on the night of his (the mob boss's) first son's birth. Before escaping he church where the showdown occured, the Predator removed its mask and was in return shot by its victim's wife, who had just finished labor. In its haste, the creature leaves its mask on the floor and books it out of there.
After it sets its self-destruct device, the entire area is turned to rubble -- but it survives. The narrator states that the Predator made its presence known to humans, left its technology behind, and didn't die in the process. Basically, our main character is shamed by the Elder and exiled on an extraterrestrial planet for 100 years as punishment.
I don't think it's bad sportsmanship, it's more just protecting the integrity of their culture.
(By the way, for anyone who hasn't played the game, I highly recommend it. Much better Predator experience than AVP 3, in my opinion. Lot of fun and a sweet storyline that, while a little overly sci-fi, fits the character's mythos well.)