I got my amateur radio license last year, and this is precisely why I haven't been able to do much with it: seemingly all the guides, even the license study materials, use vocabulary I'm not familiar with. I have two CS degrees and a solid foundation in math, but I can't understand how radios work because of vocabulary more than the math.
My uncle who's been building his own radios for over 60 years, tried to explain to me how antennas work, and even to him it comes down to "black magic".
I'm told the way they work is not really intuitive, so you just have to math it out.
Maybe I should have gotten an EE degree.
I work in software now, but I have an electrical engineering degree and started my career on a project developing a radio. Our project probably had ten or more electrical engineers on it, and only one or two of them really understood the RF side of it. It's a very specialized skill -- even EEs with >20 years of experience would describe things as black magic.
So I don't think you're alone feeling this way. Even with a good foundation in the theory and math, I think most people hit a wall with radios at some point. All the people I worked with who intuitively "got" RF stuff had been doing nothing else professionally for over a decade.
A long time ago, worked on a comm satellite program. It used a whack of tuned cans to combine high powered transmit signals with harmonics in each others' frequency bands to feed into the antenna. I once asked how they worked. The answer was 'magic'. I mean, they were physical RF filters, but no one could explain or reproduce how they worked. There was this one guy who could tighten the screws that adjusted the inside baffles so they 'worked'. No one else could.
Antennas are really black magic: optimizing an antenna requires stocastich method like genetic algorithms, simulated annealing, etc. Moreover if you want to model the radiation patterns and the electrical characteristics you need to use finite element calculation methods. So, you need a lot of computation power as antenna are not a problem that can be solved in a closed form.
Source: I almost burnt my PC on simulating a dipole array while studying for the antennas course at the university
Related: https://en.wikipedia.org/wiki/Evolved_antenna
I assure you, that doesn't go away in electrical engineering or even theoretical physics. Electromagnetism exhibits a large degree of behavioral emergence. It's one of the most well studied aspects of physics, but remains a rather convoluted and seemingly arbitrary puzzle box of nonsense especially at a macroscopic level.
Even just the theory is kind of mind expanding. I've done a little signal processing and ideas like "negative frequency" sound absurd up front and then seem reasonable once you've worked with them.
I've had my ham license for ten years, but I've only ever used a basic car-based mobile setup and my handhelds. My morse code speed is abysmal. QRP and all that are really cool, but I just use ham radio to supplement my fire/ems handheld in a natural disaster.
I'd love to see more people on the air. My advice is to get a radio with a good tuner, build a simple dipole with the online calculators, and try to make contacts that way.
It gets crazier when you start talking about things like a Tarana BN. The amount of processing in them is pretty insane.
But yeah, black magic is right!