Thinking in terms of cinematography, a battle between Engineers spaceships and Predators spaceships would give great footage and sci-fi fans love to see those space battles, with multi-coloured energy beans and particle weapons over a black-space background.
So, I think that the Engineers and the Predators were at war. Then, the Engineers created humans to be either lab rats for bio-weapons in their fight against the Predators (based on the fact Aliens are so deadly to Predators as well) or even as soldiers since humans tend to be very good in killing every other species they meet in sci-fi arena.
On alternate scenario, perhaps Predators themselves were bio-engineered. Don't you feel it is unusual that they love to hunt (as Klingons) and yet achieved such advanced technology? Also, in terms of body height, the same ways Engineers are an over-sized version of humans, there seems to be two sizes of predators. In the 2010 movie Predators, it seems that the larger Predator had captured the smaller one and was torturing him. Since these movies belong to the same mythology, there is surely a connection between these humans/Engineers Smaller / Larger Predators.
Also, in terms of chronology... We know from the movie Alien vs Predator that the several ancient cultures adored the predators, which used to come to Earth to hunt Aliens. The movie suggest an unusual timeline for the carbon dating of the alien body - 2,000 years. That means, around 2,000 years ago the Engineers decided to end life on Earth. This age was inserted in the movie, in my opinion, solely because it is a strong cultural arch-type. 2,000 years ago is believed by billions of Christians to be the time where Jesus lived amongst us.
Was Jesus an Engineer, perhaps trying to teach humans to change their ways and perhaps avoid extinction on a fast approaching judgement day? Was the accident in the WMD Engineer factory a result of accident or it may have been sabotage? By watching the Discovery channel show Mayday I've learned that plane accidents are never due to one single fault. Usually, two or more problems need to occur in a given order for a major failure to occur. A WMD installation was surely designed to be one of the safest factories but somehow it failed. Just like that cyborg at the original movie Alien bypassed the quarantine protocol and let the monster get on board, for hidden agenda motives.
We don't know why Predators loved to hunt Aliens on Earth, but it may be to train against the Engineers bio-weapon. I initially thought that virus is the deadliest thing to end life, but viruses won't break down into deep underground bunkers to go hunt you, but Aliens will do that. So, Aliens may be a more effective bio-weapon than viruses, specially considering they will die when there is no more food around, and the virus won't, and of course, radiation won't.
So, the above introduction leads us to the question at hand again - why did the Engineers wanted to kill all life on Earth? Because we became the training ground for their enemies - The Predators. Because one day, with the aggressiveness we have shown in our history, we would be more deadly than the Predators to the Engineers. We will need to wait for the next movie to find the screenwriters official view.
One last thing, please note that the female doctor was trying to ask the Engineer about the reason why humans were created and the others were becoming increasingly aggressive with her. To the point when the security guard hit her in the belly with a riffle and only then the Engineer starts killing everyone. That goes in line with my theory that humans were too conflicting beings with a past track record of hurting themselves, often for futile reasons, like "I want to know if the makers can fix me, so I won't die of old age". David, may also have said something to provoke the Engineer somehow, but that we won't know, unless you speak their language.