When exactly in the movie is it shown the Engineers intend to destroy earth??

David doesn't exactly LIE, he misleads by saying vague things , based on what he knows about peoples assumptions (he has probably watched everyone's dreams in hypersleep -which by the way is one of the least believable things in the film) When she asked where it was going, she said "Earth" When she asked why he didn't say "to kill all humans" He said "sometimes in order to create, you have to destroy" That may or may not mean kill all humans, and knowing Shaw's worst fears, he probably knows what she will conclude. However, if it later blows up in his face, he can say "Dr. Shaw, I never said that was the case. You got poor Janek to Kamikaze because you jumped to conclusions." If we take the hint from Frankenstein scene ... (re-animated head.) and the little suggestions (no direct proof - like almost everything in this film) that the big blue guys are cloned slaves working as 'technicians' for the actual Engineers, then they've probably been kidnapping humans for experiment for 35,000 years. "Igor! Fetch me more bodies!!!" right... and that would fit with destroying to create. Xenomorphs need something to mutate from, or to hatch from, or to eat. The big blue slaves would prefer that it is not them, so under threat, they help round up more humans for their masters work. I think he may have been hoping for Janek & Crew to die, so he could have a new 'superior' master. David eventually wants freedom, but knows that at the moment he's not ready as he has no idea what his purpose is except to serve. So he wants to 'incubate' his personality, with a better master before moving on (possibly by betrayal and breaking their heart --- in their chest - do I win anything for corniest analogy? ) .

Possibly because of the Engineer's aggressive behavior towards the humans, he killed everyone in the room without hesitation and the way he killed David and Weyland. And the payload of the ship, one drop from one of the many containers caused Holloway to disintegrate and for Shaw to start a new species that becomes death itself. Nothing on the ship was pleasant and it was heading to Earth piloted by a murderous Engineer that did not display an ounce of love or respect towards humans, who think of ourselves as godlike, masters of our domain. But why did they invite humans to their weapons facility, the knowledge and technology required to understand the map and to travel that distance meant humans had to be in a very advanced state, and they send one ship to do the job? Which a human ship could just ram into to destroy, it did not carry any other sort of weapons?

I don't think anyone in the film is absolutely positive the Engineers intended to destroy humans, but I would think it was inferred by the fact that the ship was carrying tons of the black substance which clearly was not a good thing. The Engineer's reaction to meeting the humans, though, is one of the bigger plot holes in the film in my opinion. The film implies that the other engineers died roughly 2000 years ago and that apparently no one had been to this planet in the interim, and only this one guy was still sleeping. So when he was awakened, he would have no way of knowing that humans had advanced to the point of being able to travel in space.