Not sure if this is the best place for this sort of question, but I'm going to give some modicum of response anyhow because I can relate to you a lot here.
My personal thought is that some people are just more inclined towards the "higher" thoughts - proofs, ideas, theorems - and others are more inclined towards computations. Sometimes you're just good at noticing the underlying details in calculations, and sometimes you're just good at noticing the nuances involved in proof-writing. Being good at math doesn't necessarily mean you're amazing at both.
I'm personally inclined towards the same things as a math major. The computational details often screw me over, more than I'd like to admit. (The fact that I have poor handwriting makes it worse - I've literally missed whole problems on tests because I misread my own handwriting!) My proofs and such are usually pretty good and I have an understanding of the ideas, but sometimes I get too ahead of myself in the calculations. Hell, not 5 minutes ago, I had to correct a small error I made in helping someone on here on MSE (and sadly it's not my first time doing that).
Anecdotally, I feel like this is a remnant of my middle/high school math team competition stuff, where speed was emphasized. There was a "speed math" sort of thing where we had to solve problems very fast in order to get points. I was the good one on the team early on but at some point - despite remaining the good one for other reasons - the speed lent itself to errors.
What has helped me curb this somewhat and maintain my grades was double-checking my work, going line by line, trying to justify each and every bit - both for calculations as well as proofs. It's not perfect and you have to consciously ensure that you don't get hasty again, but it has helped me quite a bit. Heck, reworking it all over again - but carefully - helps, as would checking your answer. (Checking being, for example, trying a few values for your solution, differentiating an integral, trying to "break" your proof with counterexamples, whatever the context would demand. And in reworking a problem, trying to not "bias" yourself by basically copying down your previous solution - reworking it a different way if at all possible, even!)
It's not much and it might not be even possible if you don't have time - it depends on the testing environment. I've had exams where I've had literally hours to spare, and others where I was working right to the very end, so it all depends. But that's the main thing that I've been trying and it has helped somewhat. Just slowing down, checking your work, reworking if possible ... it's small and too often said, but it really helps if you can maintain the slowing-down bit.
I don't think it's so much a matter of maturity or intelligence or skill or anything like that. Personally, I'd say skill is only in part the computational abilities, and moreso are the higher things like proof-writing. (Thus why I also think it somewhat absurd that you lost all of the points on that question for a simple mistake.) I feel like if you understand the ideas and proofs and theorems and whatever, that's like 80% of the battle. Anyone can plug-and-chug - I've done it without even understanding the material or where the formula comes from - but understanding the material is truly the important thing. At least to me.