Probably the biggest problem is the state-space. Software is highly non-linear and discontinuous, unlike for example a bridge, or most other physical objects. If you change or remove a single bolt from a bridge, it is still the same bridge and its characteristics are largely the same. You need to remove quite a number of bolts for that to change, and the effects become noticeable before that (though they do get catastrophically non-linear at some point!). If you change one bit in a piece of software, the behavior is completely unpredictable. It could be the same, it could just crash, it could quietly corrupt data. That's why all those corner cases in the layers matter so much. Again, coming back to the bridge, if one beam has steel that has a slightly odd edge-case, it doesn't matter so much, you don't have to know everything about every beam, as long as they are within rough tolerances. And there are tolerances, and you can improve your odds by making things with tighter tolerances than required. Again, with software it isn't really the case, discrete problems are much harder than continuous ones.
You can see this at work in optimization problems. As long as you have linear equations of real values, there are efficient algorithms for solving such an optimization problem (simplex typically runs in linear time, interior point methods are polynomial). Intuitively, restricting the variables to take only integer values should be easier/quicker, but the reverse is true, and in a big way: once you have integer programming or mixed-integer programming, everything becomes NP-hard.
In fact, I just saw this in action during Joe Spolsky's talk "You suck at Excel": he turned on goal-seeking (essentially a solver), and it diverged dramatically. The problem is that he was rounding the results. Once he turned rounding off, the solver converged to a solution fairly quickly.
The second part that they touched upon, is that it is all abstract, which I think is what they were getting at with the idea that is 100% built. Software being abstract means that we have no intuitions from physical objects to guide us. When building a house, everyone has an idea of how difficult it will be to build a single room vs. the whole house, how much material it will take etc. With software, not so much: this one seemingly little sub-function can potentially be more complex than the entire rest of the program. Even when navigating a hierarchical file-system, there is no indication of how much is hidden behind each directory entry at a particular level.
The last part is related to the second, in that there are no physical or geometric constraints to the architecture and connection complexity. Again, in a physical system we know that something in one corner has very limited ways of influencing something in a different corner, and whatever effect there is will be attenuated by distance in a very predictable way. Again, in software we cannot generally know this. Good software architecture tries to impose artificial constraints to make construction and understanding tractable.