Nearly nothing to add but agreement on leaving this instructor and never going back.
Only this:
With that said, as a fellow software engineer, you likely do not want a standard CFI.
Based on the analysis in your post, you will focus on the numbers before you focus on the feel in your hands. (this sounds rather familiar)
Therefore you need someone who is analytical and likes to fly by the "numbers". Once you have the numbers, the feel will come later. My suggestion, look for a CFI who is an engineer or works for the airlines. Explain that you are analytical, and need to get the "numbers" first. If the CFI does not catch your drift, keep looking.
Tim
Engineers have a tendency to learn this way, and I've seen this before. Agreed.
You are looking for perfection and aiming for the number, I am in software too and still do the same thing , but cut urself some slack, there is nothing wrong if your target speed is 90 and u are at 87. Don't try to correct it, think that's mostly lead to over correction. At least that was the case with me
I find it more productive if someone is a "numbers" learner to just use the FAA's "numbers" and work from those. And most analytical engineering types appreciate ticking off checkboxes, too ... and when presented with a numerical standard to hit, they often are quite self-motivated.
So perhaps with your next instructor, ask them to look over a copy of the ACS with you and go over the required performance numbers in the ACS and build a list of things (to keep your brain happy) that *their* syllabus is working on for you. Map the plan out for each flight but be willing to follow their lead. They know what you don't know.
Instead of looking at it as an *exact* number, look up the *requirement* in the ACS. And then expect your instructor to want to eventually see you do it *better* than the ACS standard for personal motivation. If the standard says +-100' for altitude, shoot for +-50'. Give yourself numerical goals. As you get better at it, make the goal harder. +-20'. Then +-10'. Same with airspeed.
Use the numbers provided instead of "that's about right". This works better for most engineers. Phrases like "It's supposed to be 90 knots but 87 is okay" don't map as well to the engineering brain as "the airspeed standard for this portion of the flight is -0,+10". Slow is sub-standard so if you have to make a mistake here, be a little fast.
And remember the ACS standard is a *minimum* standard. You can always choose to fly better than the Private standard.
Make sense to use the FAA ACS numbers? Give that a try. I think you'll like it.
If not, there's other ideas where that one came from. And that's the disappointing thing about the instructor you ran into first. All instructors should have more than one teaching tactic up their sleeve.
But I think you'd be the sort who would like a number challenge. Hit the FAA ACS standard. It'll be frustrating at first and your confidence will take another hit (expect it!) and then you'll get better at it and you'll want to tighten it up well past the minimum standard (and your confidence will rise).
If the instructor manages the daily expectations right, you'll walk away knowing you did a good job on some things and other things need work. Don't dwell on it, just go up again and work on the harder stuff more.
I understand this engineer mentality. It happens to me. And I have a number of engineer pilot friends. It takes a number of hours for us to relax at first and then start "feeling" the airplane instead of mechanically chasing headings, airspeeds, and altitudes. The sooner you relax and feel the airplane moving through the air, the sooner you'll go from following numbers to aviating.
Oh, and expect your instructor to cover up all the instruments to *challenge* your numbers brain eventually. Because you *can* fly the airplane without staring at those gauges. Mine used a jacket. Covered the whole panel and said, "Ok, now feel the airplane, and fly the pattern, and land." You'll have to go through that. And it'll be memorable.