I'd just add that my squat experience has also been frustrating, nonlinear and defying of logic.
I started lifting about 15 months ago. Within 3 months my squat shot up from 60 --> 110. But I knew my form was off and any time I added a couple pounds my form would go from "iffy" to "bad". I deloaded completely and focused on form for 3 months, working back up to 110. I'd love to say that after that "and then everything was fixed!" but no. I still plateaued hard, except I plateaued at about 120.
A few things that helped get me out of this funk:
1) after the 7 months of floundering with poor form and stagnant weight, I adjusted my stance to be wider. I am short and have short legs and a long torso. For some reason, once I widened my stance just past my shoulders (like only about 4" wider than my previous stance), I started FINALLY understanding how to push my ass out, keep my back up and not good morning my way out of the squat. With a wide stance you literally cannot make these mistakes or you won't get back up - that's why a lot of people recommend goblet squats to start. This worked for about 3-4 months, and I again worked my way up form about 90 lbs to 120 lbs with this new wider stance.
2) Weight got harder to add again at 130. I started trying the normal stance again. This time, I guess from the experience I had re-teaching myself how to squat properly with a wider squat, the narrower stance made WAY more sense to me. Before, I wasn't going to parallel and I was bending with my back in order to bottom out. Then I would good morning my way back up, rocked forward on my toes. The wider stance basically made this impossible. Then when I went back to the normal stance, those mechanics were still there, and it all suddenly made sense. HURRAH.
3) I switched from SS to Madcow after ~12 months (I had to take some breaks due to injury during SS which is why I waited a bit longer to switch). For me I think, aside from the form, this was a huge factor in addressing my mental block with the squat. Anything over 130 was unthinkable, especially for 3x5. If I ever did a set with less than 3 I felt like a huge failure. What I love about Madcow is that it's still MWF, which works for my schedule, and you still squat every workout, but each workout varies in intensity and endurance. The "light" day requires working your way up to 3 reps at your heaviest weight. That's it. So right now that's 130 for me, and trying 130 for only 3 reps is COMPLETELY mentally doable versus 130 for 3x5. Then, the "high intensity/high endurance" day would be 4x5, with each rep increasing in weight (so like 100x5, 110x5, 115x5, then 125x5). Since I've just done the 130 the previous workout, 125 seems like a breeze - I can't psych yourself out like "I WILL CRUMBLE AND DIE" because I know that I already lifted heavier weight last time. The next week, you increase the weights. I already did 3 reps of 130 and didn't die - I can at least try for 3 reps of 135.
The point of all this is squatting is a journey. It's hard to get the form right, and sometimes your weight is increasing with bad form, and then when you fix the form, instead of just continuing in a linear progression, you have to start basically from scratch. Sometimes you have to try weird and nonsensical things (wider/narrower stance). Sometimes you have to adjust your brain (whether switching programs, sucking it up, or teaching yourself to fail with a few practice drops).