Signed, Not an aerospace engineer ;)
On the other hand, there's nothing "engineering" about software engineering.
And I would tend to agree with your second point. We might occasionally borrow some formalism and organizational structure from our engineering cousins, but it's different in enough ways that it probably shouldn't bear the same moniker.
I am just allowed to try pressing the red button several times a day instead of once every two years.
Comparing the number of parts underestimates the complexity of a computer system, of course, because the software is a machine with a vast number of parts, on top of the hardware.
In other words, I'm on the side of those who say software is hard to get right for good reason, and not because the practitioners are less competent.