Claiming diagonalization cannot separate P and NP conflates one well-defined barrier (relativization) with an exhaustive prohibition, thereby overstating what BGS actually proved.

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BGS(in computational complexity history): Short for Barak, Goldreich, and Wigderson—three computer scientists who proved an important result about the limits of certain proof techniques in complexity theory.
Conflates(in argumentation and logic): Treats two different things as if they're the same thing, or mixes them up in a way that causes confusion.
Diagonalization(Computational complexity theory): A proof method employed in establishing the undecidability of the classical Halting Problem, which can also be used to prove separation results between complexity classes such as P ⊊ EXP
P and NP(as the two categories being separated): Two classes of computer problems: P are problems computers can solve quickly, and NP are problems whose solutions are quick to check once you have them (like a sudoku puzzle—hard to solve, easy to verify).

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Claiming diagonalization *cannot* separate P and NP conflates one well-defined barrier (relativization) with an exhaustive prohibition, thereby overstating what BGS actually proved.