I've been filtered by this for eight years now and still don't get it (80-85 IQ, btw). I'm not an intuitionist or anything, for an intuitionist accepts contradiction-based proofs not relying on double negation, whereas I don't get those either. I've blown around $6,500 USD on Zoom calls with undergrad math tutors, and it's just not clicking. Here's a transcript of a recent conversation:

TUTOR: "So assume P is true."
ME: "OK."
TUTOR: "Now try to find a contradiction."
ME: "Why would I do that?"
TUTOR: "So you can show that P is false."
ME: "I'm assuming that P is true, right?"
TUTOR: "Yes."
ME: "So per my assumption, how can it be that P is false?"
TUTOR: "Well, you assume that P is true and then you reason from the truth of P and see what happens."
ME: "OK, I assume that P is true. From the truth of P, it follows that there is no proof-by-contradiction process by which P can be shown to be false."
TUTOR: "No, that's not how it works. You don't actually know that P is true."
ME: "I'm just to assume that it is?"
TUTOR: "Yes."
ME: "I'll try to work on it."