I struggle at proofs but can do statistical inference or actuarial probability problems like Hogg/Mckean/Casella/ODEs/Calculus because I find that the exercises are similar to the examples.
In a proofs based class, I can't see how the problem I'm doing is similar to any classroom or textbook example.
If I work hard, I can memorize a proof, and some basic set theory proofs about deMorgan or powersets or induction proofs or cantor snake or the infinite many primes, injective, andsurjective proofs make sense. When I first learned doing proofs, I spent 3months asking about how to prove deMorgan's laws and figured how to prove deMorgan's laws by the 4th month.
However, proving that things are cauchy or converge, or doing abstract algebra with lagrange's theorem I'm lost. I trust the well-ordering principle, but to prove something is an injective subsequence is beyond my ability. I tried number theory and take class made no sense. I didn't understand CRT, euler phi function...
Memorization alone won't let me pass proofs beyond an introductory course because I won't be able to do the homework or take home exams and because other's can't always give me the answer on every problem.
At this point, I realize that I can't find a white collar job unless I figure out how to do proofs to become a machine learning expert, so I'm wondering what I need to do. I could resort to learning a blue collar trade.
Some graduate programs require proofs based classes even for statistical programs. While the biostatisticians may disagree about how much math is needed, I'm sure the cutting edge of machine learning is all done by math phDs who require proofs knowledge in their programs.
I think I would have been better off studying Biology or Psychology or Geology and maybe dabble in medical organic chemistry/biochemistry because those are purely memorization but it's too late to change degrees. Even Physics might be possible because it's manipulating examples in the textbook to solve the problem.
Some person expert in math told me they think I can do proofs but it wouldn't be worthwhile to learn anymore and said I should study financial Accounting instead. Were they just telling me that I can do proofs to make me feel better?
I don't think this is really a question about math, but I hope that we can leave your question up. I sense from your post that you're feeling lost and hurt, and I'd like to (try to) help.
I want to be both kind and blunt. It seems like the crux of your problem might be a problem of maturity. Reading into your post a bit, it seems possible that up to this point in your mathematical career, you have succeeded in your math classes by doing a process like this:
If that is indeed what you've done, two things are unsurprising: (1) this used to work, and (2) it doesn't anymore. The unfortunate fact about this process is that whatever it is, it isn't math.
If you've been trained so far to believe that the process above was appropriate, and that doing that is what constitutes success in math, then that conviction is the essential problem here. What it means to do math is decidedly not to do a process like the above. Instead, mathematics involves something much harder to grasp; it's careful thought, exploration, experimentation, finding patterns, constructing arguments, and things like that.
Imagine a person who believes very early in their schooling that they are very good at math because they know all their multiplication tables. If you give them a pair of two-digit numbers, they can multiply those numbers quickly and efficiently, and they can give you a correct answer. And yet, somehow when algebra is introduced into the discussion, they are lost. They cannot conceptualize what it means to have an unknown $x$ and to solve for it symbolically. This person has mastered arithmetic, but algebra remains mysterious to them.
The problem I described above is not your problem, of course, but I think it's analogous to your problem. You're having a difficulty making a transition to the next level of what genuine mathematics is. Please let me affirm this first: Math is hard. It's OK to struggle with it. I have, as has (I believe) every other poster on this board.
If we accept the premise that your most serious problem is a lack of understanding of what math is, I think a close second is a crisis of confidence. You approach this issue with some language that concerns me: you're worried that others are lying to you "just to make [you] feel better," you worry that you "don't have the skills to obtain a lucrative job," and so forth. I will warn you: If you believe these things, they will remain true. You can grow your skills. You can gain new abilities. You have more potential to adapt than you believe.
I could tell you stories about times in my schooling that I doubted myself. I could write pages just about the time I had a panic attack, collapsed on the floor of the bathroom in graduate school, and contemplated my future as a mathematician while trying not to vomit. (Spoiler alert: I now have a PhD and am a tenured professor at a liberal arts university.) I think the most useful thing that I can do right now, though, is just to emphasize that nobody starts out as a finished product. Everyone struggles, and everyone must go through the painful acts of learning and growth.
Only you can decide what the future holds for you in mathematics. I would love to tell you that I believe that every human holds the same capacity for mathematics; however, in truth, I don't know if that's really true. What I do believe, though, is that every human holds the capacity to do enough mathematics, whatever that means for them. Consider the useful analogy of running a mile. I believe that no matter how hard I train, I will never be able to run as fast as Olympiads. I certainly lack the physical qualities needed for that, but I think I probably also lack the grit and determination required to do that. However, I can run a mile in 8 minutes, and in the past, I have worked hard to get that down close to 6 minutes. The point is that even though I never had a future as a professional runner, I shouldn't think of running as something that I'm not good enough to do. I can run as fast as I need to for my purposes, such as chasing my kids around or making it to meetings across campus.
I believe, without knowing much about you, that you can do as much math as you need to do. Only you can decide how much math that is. But I promise you that you will be limited by your own imagination if you allow yourself. It's probably true that you need to change your study habits, and perhaps even your entire approach to mathematics. But you can do those things.
I would strongly encourage you to speak with people you trust about this. Start with friends or family; branch out to an academic or career advisor. Consider also a counselor or therapist, and do not feel shame about doing so. Gather as many opinions as you can. Retain the ones that are useful, and discard those that aren't.
I'm sorry that you don't believe in yourself, and I'm sorry that you're hurting. Please remember that you can adapt -- either by improving your skills in math, or by finding something more suited to your interests and skills.