It's a fundamental part of our physiology that we have to consume a certain quantity of macronutrients to support our metabolic processes. If we don't, then our bodies utilize existing stores of macronutrients like fat and muscles, breaking them down and converting them to usable energy to meet the deficit. This causes you to lose weight, as you drink water, metabolize your fat and muscle tissue, and then exhale carbon dioxide, and excrete waste products. You're literally breathing the weight out.
You find motivation so that there's something preventing you from stuffing your face with cake every day. Then you spend a few months iterating while you figure out what you can build a diet out of that will leave you sated and allow you to cut calories. This is where your metabolism, psychology, etc. come in. Once you have that dialed in, and you may arrive at it without counting calories if you're careful, then you will start losing weight.
Weight loss requires a lot of self-awareness and attention to what you enjoy or don't enjoy about a variety of foods. Somehow, through some series of test meals, you figure out that you really like raw bell peppers, but only with salt, or that the only thing trail mix is actually good for is making you hungrier(this is something I struggle with).
This greatly describes why so many people have a problem with the blanket statement "Eat less calories than you burn and lose weight.", because it implicitly contains the crux of the matter.
There is no such thing as a single, straightforward "calorie goal that lets you lose weight without feeling like crap". It varies wildly depending on the composition of your diet (which is even different from person to person) and accompanying factors like amount of physical excercise, sleep patterns etc.
And those are the deciding factors. The calorie deficit is a prerequisite, but the difficult part is in finding a way to sustain it. (I mean, you go there yourself in the following paragraphs.)
But the statement alone is borderline useless and actually quite condescending to anyone with a modicum of diet expierience. It's like saying "Answer enough questions correctly and you'll pass the test." Duh, No shit, sherlock.
This mantra annoys me, because it's like saying that to go to space, all you need to do is to burn rocket fuel and keep the nozzle pointed down (and then to the side).
It's technically true, but every single sane person know that it's true, and it doesn't really help you get to where you want.
It ignores how food affects motivation, digestion, metabolism etc. You can technically loose weight eating only sugar, but you'd find it impossibly hard due to the way the body is wired.
Generalizing to the obvious/trivial is not useful.