Just another analogy to maybe help explain why #EverythingIsTrickyNotJustRockets (in addition to the great answers already here).
Take Formula 1 racing. It's a sport with some extremely complex machines, built to the very edge of engineering and manufacturing capabilities to give as much performance as possible. Just like rockets. Others have mentioned airplanes, but those are generally built to be safe and comfortable, too. F1 cars just have the imperatives of "win race" and "try to not kill driver". Again, much like rockets.
There's plenty of experience with race cars. F1 cars as we see them today (rear-mounted engine, monocoque chassis) have a lineage back to the 1960s, and cars in general have of course been around much longer. And there's a lot more F1 racing than rocket launches, so there's more practice as well.
Even so, take a look at any race from last year's season. For instance, the Malaysian Grand Prix:
Of 20 cars, 5 failed to complete the race. And none of this was due to plain ol' collisions. One car spun off the track, so you could call that driver error, rather than #RacecarsAreTricky, but the remaining 4 were all due to technical issues. Specifically: Brake failure, turbo failure, power unit failure, and fuel system failure.
So, at best, that's still a failure rate of 20%.
That's a pretty common failure rate in a Formula 1 race. There're always cars that break down during races. And they're just cars! Yes, they're advanced and insanely complex cars, but things like brakes, fuel systems, turbos - those are all things that regular, everyday cars have too. We know these systems well; the F1 versions are just the very best that money can buy. And yet they fail.
Compare that to rockets, which have nothing in common with everyday vehicles, and where there's just nowhere near the same amount of practice to begin with.
Now, if we have a hard time making a car go reliably around a squiggly circle for a few hours, it's amazing that we're able to make rockets at all.
To respond to your earlier comment:
I was under the impression, that the most fragile parts in any construction should be known at the time of designing it, thus the question of project success would boil down to material and engineering quality. Is that impression totally wrong?
Alright, let's say you build a liquid fuel rocket. You know exactly how much thrust it'll produce, and you make the structure strong enough to withstand more than that. Good safety margin. You use the best materials and all that. It's all completely by the book.
Then you ignite it. Inertia keeps the rocket on the ground at first, with the engines pushing hard against their support struts, so the struts flex a little. They have to: They can't be infinitely strong. But you've accounted for that, so it's fine.
Fuel combustion is almost perfect. Almost. You simply cannot guarantee that it's 100% perfect, because it's a chaotic, violent chemical reaction. However, it's well within tolerance, and the rocket takes off beautifully. Just as planned.
But that tiny bit of combustion instability causes some vibration. The vibration makes the engine supports flex a tiny bit more. Nothing to be alarmed about, they're built for it. If they weren't, they'd snap instead of flex.
But when they flex, the fuel line to the engine also gets compressed and stretched too. This changes the flow rate of the fuel, which changes engine pressure, and, in turn, thrust.
So now, your engine's initial combustion instability has has caused more instability, and more vibration. The engine starts to vibrate more. It doesn't (yet) flame out or explode or anything, but it's not producing a stable amount of thrust. Engine supports and fuel lines flex more and more, making the problem worse and worse.
Sooner or later the struts or fuel lines flex too much, and, in technical terms, rocket goes boom. Or maybe you've accounted for a lot of vibration in the struts, but the entire body of the rocket starts shaking and bending like a pool noodle from all this vibration, so it snaps in two, and... rocket goes boom. Or a million other things could break as the vibrations grow and grow. Maybe the engines just experience fuel starvation, flame out, and the whole thing falls to the ground (and goes boom).
This type of situation is called a pogo oscillation, and it famously plagued the Saturn V rocket for quite some time. It's something that any large rocket has to deal with. And ways have indeed been found to deal with it. But before it was first experienced, who would have thought of it? You'd pretty much have to experience a failure first. And then you can fix it.
In the end, your design will contain assumptions. Assumption like "thrust is X". True - until the vibrations started. After that, you might as well assume that "thrust is infinite", but then you'd have to make the struts infinitely strong (good luck with that). Or maybe you have an assumption like "liquid fuel settles at the bottom of the tank". That's true if there's gravity (and the rocket is upright). It's true if there no gravity, but the rocket is accelerating. But it's not true in microgravity with no acceleration. There, the fuel sloshes around, which can causes problems all on its own, besides the fuel not being near the pump intake. Of course, you've already thought of this, so you add ullage motors to add a bit of acceleration, and make the fuel settle again.
Except now, of course, you've actually just strapped another set of rockets to your rocket, and you have new problems and assumptions to deal with, because #RocketsAreTricky.
Your comment was itself based on an assumption: That it's possible to know everything.
Edit: As Michael Kjörling adds in the comments, Apollo 13 experienced pogo oscillations on launch. Even though the engineers knew of the phenomenon at this point, they were still surprised by the oscillations, because "they were amplified by an unexpected interaction with turbopump cavitation." That's the sort of complexity you have to figure out.
That article is worth a read, but its references are even more interesting. It cites an aerospace industry publication, that just happens to contain the aptly named article: That's why they call it rocket science, which also attempts to answer the question: "Why is it so hard to launch a rocket into space with absolute assurance of success?". Pretty much exactly the thing you're looking for! Among other things, it offers this quote:
Launch system designers base their designs on the best data available—but sometimes, the best data are just good estimates. True measurements of the launch environment can only be obtained in flight, and that’s hardly an option at the design stage.