I agree with the sibling comments, but let me add a few ideas. Let's not even worry about the bureaucracy, safety regulations, etc. for a "Skunk Works" phase. The safety and reliability stuff is even harder, but just the first phase of building anything that flies is really hard.
Aircraft design requires truly careful engineering. There is very little leeway. EVERYTHING is a trade-off. You have huge forces and need very light weight. You add a pound of structure to tolerate the loads, now you have more loads and need more power all of which adds weight, requiring more fuel to make range. All of that requires more structure, which adds weight. To find a workable design that "closes" is hard because there is a very small corner of the design envelope that will even work.
It's also hard because when working at these extremes of what is even possible, there is no room for failure and you can't just add reliability by brute force (adding more power, more metal, etc.). There are fine margins because you can't afford thick ones. And to live with these fine margins, you must have extremely tight manufacturing tolerances and predictable performance.
Aircraft are also a very complicated system. The physics are complicated, the behavior of all the required subsystems is complicated.
So now, you have to do the most precise careful engineering you can think of, across a set of super complicated interdependent systems.
So all of this costs a lot of money, and at some point - for a new design - it has to take off for the first time. At that point, basically nothing can go wrong. You can't exactly fire up gdb, find the bug and recompile. There is no edit-compile-test cycle (well, or it's a very short cycle).
The only thing that seems harder is rocket design. Actually turbo-pump design for the engines for the rockets.
ok I see but at the same time, I guess there is a ton of knowledge about previous planes floating around. You don't do it from scratch, do you ?
Processor are really hard to do, as well as software for physics simulation, as well as a ton of other things. But for both of them, I can confidently say that nobody starts from scratch: it's improvements upon improvements and from time to time, a bit of breakthrough...
I do understand that the safety aspect is pretty specific and really tough to get right.
> I guess there is a ton of knowledge about previous planes floating around. You don't do it from scratch, do you ?
Well, derivative designs bring their own problems. Also a double edged sword. Making significant mods to a complex system is often even more difficult. There's a lot of analogy with software and computing. Take 737-Max for example. Obviously boeing royally screwed that up - but mainly because their business people underestimated the difficulty and tried to patch over it and take short cuts. That itself is a hard problem: a commercial company does eventually have to make a profit.
And yes, absolutely there are new greenfield designs. If you need a Cessna 170, you don't usually start from scratch. But one reason to start from scratch is that you are pushing the envelope even further because of new materials, new requirements, etc. So more problems.
As someone who is in airplane engineering, the biggest barrier today to building a new aircraft is regulations. But if we completely ignored regulations, and you were building a mostly aluminum aircraft with analog avionics and the goal was just to get it to fly (nevermind things like designing for fatigue), then no it wouldn't be that difficult conceptually on paper. However, manufacturing would still be the bottleneck, and that is still challenging today (tolerances, QA, technical expertise).
However, if you were designing and building a new aircraft to meet the latest Part 25 regulations for passenger transport, it's almost insurmountable. There's a reason why there are so few aircraft OEMs.
And to go along with it for Part 25, you're pretty much guaranteed to be doing something "thinking outside the box" if you're doing a clean-sheet design, because the current models (737 Max8, A320, etc) are all pretty darned close to their local optima. No one's going to do a clean-sheet design for 5% more pax and 5% less fuel burn, they're just going to riff on something that already has type approval so that a good chunk of the regulatory burden is already mostly taken care of.
Structural design.
Design for manufacturing and assembly.
Power and drivetrain.
Control systems and actuators.
Avionics.
And then get all of these to a reliability level where you feel comfortable with a single failure causing high likelihood of multiple human deaths.