--movie spoilers all over this text--
If you accept H. R. Giegers' original works and his commentary on it as canon, we know at least two things about the engineers:
Like most of H. R. Gieger's work they were or could be cyborgs or similar man-machine mixes. The pilot chair the engineer enter and gets enveloped in at the end is a replica of the fossilized pilot chair and pilot from the first alien movie. Giegers intention for it was to depict a pilot who was his pilot role to such a degree that he had fused with the machinery and ceased to be anything but the pilot.
They attached a religious significance to the alien monster. In Gieger's picture below, the overarching cyborg woman is a reference to the portrayal of the egyptian goddess Nut, which was the goddess of the sky and gave birth to several other gods. Gieger's picture then shows a goddess sending the alien eggs down from the skies.
It is then a small leap to imagine that the engineers, being already in a symbiotic relationship with their machines and revering the aliens, also were in some symbiosis with the aliens. In fact, have you noticed how there were only male engineers?
Gieger originally played a lot on allusions to sex. He was a designer for the first Alien film and his original design of the egg had the top split along a single slit in what became a comically obvious allusion to a vagina. (*) The face-hugger force the victim to deep-throat in an obvious rape simile and then the victim, often male, is forced to undergo a gestation and "give birth" to the alien. In short, the vagina-egg force the victim into taking the role of the receptive sex.
So imagine, here we have The Engineers, a species which has lost its females and now only reproduce via machines. (Plenty of cyborg fetuses in Gieger's art btw) But they revere as mystical the ancient "female", which is symbolically opposite both to males and machines. (**) In its contained revered form the engineer's "female" is abstracted away into a sticky oozing fluid with worms. It doesn't get more biologically icky than that after all and probably horrifies the engineer-machines like the depictions of the mutilated corpse on a cross are meant to do for christians. This goo doubles as paint for their mystical paintings.
A devout engineer may volunteer to "mate" with the goo. Only then do a true biological organism with its own lifecycle appear. Note that in Prometheus the protagonist only births a face-hugger, which must then infect another organism before an alien occurs. The aliens lay the eggs and have queens and drones. Recreating this two-sexes fully biological creature is seen as a holy act by some engineers.
We can guess at a schism early in the religious history of the engineers. They start out as in the opening scene of the movie, with the creation of biological life as the holy act. Then they split into two factions. One with a mechanical leaning which worshipped the machine-inspired alien monster and sent it from the stars to many destinations, preying on the life seeded by the original religion. (A semi-canon comic link an early extinction of life on earth with aliens) Then there's one faction with a sapient leaning which recreates life in their own image, including humans. Trope-wise they suffer from the "Gepetto Syndrome", which is sometimes used in ridicule about men who, unable to create life themselves, obsess with robotics or artificial life. Being a Gepetto they fall in love with their own creation, can find no fault in it or think they can just fix its faults like you fix a machine.
The reason the Engineers turned on us are then either that we were a failure in the eyes of the humanoid-makers and they turn on their own creation in anger (the movie characters' hypothesis I think) or that the engineers in Prometheus belong to the alien-faction and regard humans as sacrilege committed by the other faction. An interpretation is that the engineer awoken in the movie rips the head off David because his question implies that the engineer would be one of the heathen humanoid-makers. Prior to that the drowsy engineer hopes that the humans are there as devoted and willing vessels for the alien "incubation".
The Engineer ship is then one small part of a giant religious war machine where the alien-breeders seek to eradicate the works of the humanoid-breeders.
So what about the head? Others have pointed out that the head is not on the ship itself. The room is a church and they worship the original humanoid "mother species" which created the machines and their male-only descendants. The head is a "mother" (note machines are birthed in the head of the inventor) but is depicted as the male's faces with a few streaks of technology because the engineers have lost all recollection of how their females actually looked.
Ridley Scott: If you're reading this, I'll trade you the plot for a Gieger painting and a face-hugger plushy. :-)
(*) The vagina design was turned down by the producers, citing catholic audiences as a reason. (Really I think it was just too gross, but put it nicely to the artist :-)
Gieger then changed the design by keeping the lips of the slit but making it into a cross instead. He writes that he was quite amused that he had hid the vagina by merging it with the sacred symbol of the prudes he re-designed it for.
(**) Female as base body and male as logical spirit is unfortunately a common underlying theme in much art, even today.