And, in reading what Elon says in that press release, it's clear why rocket science is indeed as difficult as the cliche claims.
It's not that designing a rocket is necessarily all that difficult. An average rocket and an average car probably have similar amounts of engineering work in them, and most of that is just a lot of hours spent on simple things. Fundamentally, you mix oxygen and fuel, burn them in a chamber that's attached to a diverging nozzle, add some control systems that we've known how to build for half a century, and that's what it takes to build a rocket. It doesn't even have to have automatic power cupholders.
The problem, fundamentally, is testing. Because that's how we engineer things -- we build something we think will work, try it out, see what doesn't work quite right, tweak it a little bit, try again, and eventually get all the bugs worked out.
It's easy to do that with cars. Cars sit on the ground; the power cupholder is going to work the same whether you're sitting still in the lab or driving down the road. Maybe a rough road will affect it, but you can put it on a shaker in the lab to simulate that. And when you're testing the whole system -- if the wheel falls off going around a corner on the test track, you stop, haul out the jack, find the lug nuts, put the wheel back on, and drive it home. (This happened to my brother once, not on a test track.)
Airplanes are a bit harder, but even so. A lot of pieces of airplanes get tested out on other airplanes. Want to see whether a jet engine actually works up at 35,000 feet and Mach 0.85? Boeing has a 747 they use for that; they take off one of the engines, and replace it with the engine they want to test. It looks a bit funny, but it will take off on the three engines that we know work, and if the test one doesn't work right, no harm done. And when they build the whole plane, they can run it up and down the runway a lot, and make short hops once all that works, and test it a little bit at a time. And, besides, we've been building airplanes for a hundred years; at this point, the new ones aren't that much different than the past ones, so most of it's made out of things that we know work.
On a rocket, though -- sure, you can test out the stage 1 to stage 2 separation in the lab. Except that, on the real rocket, it's going to be happening after the rocket's gone from 100F to something a fair bit hotter than that (I think) to something quite a lot colder, with a lot of force applied to it and then moments later dropped into weightlessness, and this is on something about the size of a small apartment building. You can't test that in a lab. You can't test that by carrying it around under an airplane, even.
Nope. To test that, you have to build the whole rocket, and set it up on the launch platform, and launch it halfway to low earth orbit. And, from SpaceX's example, it looks like that costs quite a significant lot of money and takes about a year to do all the rocket-building to get to that point. And, if (say) an attachment on the engine fails and causes a fuel leak because the salt air on the launchpad at your atoll corrodes it differently than what happens in your nice dry test facility back in SoCal and then the engine catches fire at launch and you only get 35 seconds into your flight, well, hopefully you'll get to try out that stage separation on next year's launch instead.
And you'll get surprised, too. On the second launch, the thing that broke (which was pretty near the end of the launch, so it was a good launch; lots of things got tested!) was that the oxygen in the stage-2 tank sloshed a lot more than they expected. Sure, you can simulate an approximation of that, with leading-edge CFD software that gets you something kind of like the right answer, but that depends on having the right inputs. And, up in near-orbit, the engine shut down happened a bit more quickly than they thought it would -- and, of course, this is all different from what it does on the ground! -- so it jostled the tank a lot more when it did that than they expected it to. It's a complicated system, and it's all connected.
That's why rocket engineering is hard. Any engineering -- rocket or otherwise -- involves a lot of trying out things and tweaking them. Most of the time, you can do that quietly in your shop, building up the thing a bit at a time and adjusting as you go. With rockets, there's lots of stuff you can't test without a full flight test, and a full flight test means building a whole new vehicle and spending months getting everything ready and filling it with tons of fuel and then launching it up into the stratoshpere with thousands of people watching, where it will probably end up exploding for one reason or another, probably before it tested all the things you wanted it to test. And then you get to pick up the pieces out of the ocean and do it all over again.
With that sort of test cycle, even designing a paper airplane would be hard.