You seem to have it pretty well-covered. The only other thing I can think of is that you might hurt them as you lift them.

Terror is probably the main reason.

It's a cry for help. They learn it at their birth, when they fall out of the nest. Falling out of the nest is not the worst thing (in case they survived). The worst is when a predator comes by to eat them. In case a predator catches them they cry for their mommy to save them. I once picked up a young crow which hurt it's wing. When I picked the crow up it started making a squeeky sound and immediately mother crow came out of the tree and started attacking me by flying close to my head trying to pick me. 

Same counts for grown-up birds, it's an automatick response because they are very vulnerable to predators and by crying out, they warn other birds for predators.

I'll think you'll find as much scientific fact behind the answers given so far as you would sacks of elephant faeces on the surface of Mars. The answer you want is a combination of A, B and an E which I'm about to provide.

If you look at the literature around audio-analytical studies of bird calls you'll find that there's an underlying frequency that is common to all bird calls. The way it's embedded in each bird call is analogous to carrier frequencies in some radio transmissions. The frequency is ultrasonic and therefore not audible to the human ear. However it's non-audible quality is not the instrumental part of the defence and it was some years before the significance of this static frequency was theorised. The frequency in question has been theorised as a common resonant frequency in relation to the skull density of several common bird predators. This is very apparent in many carnivorous rodent species and their evolutionary descendants. The theorised mechanism is that the bird call causes resonant vibrations in the skull of the predator which confuses and distracts the predator long enough for the bird to attempt an escape. In a now famous experiment to demonstrate this, a group of European researchers exposed the skull of a Rattus norvegicus (brown rat) to the artificially amplified call of a common sparrow. After only a few seconds stress cracks were noticed along the top ridge of the skull. As I've hinted at this is still considered a theory albeit one that has some very strong backing from many of the worlds leading ornothological biologists and animal behavioural experts.