Why do intuitionists reject some nonconstructive mathematical proofs?

Intuitionists, a school of mathematical thought founded by L.E.J. Brouwer, reject nonconstructive proofs because they contend that mathematical objects must be mental constructions rather than abstract entities existing independently of our ability to define them.12

The primary reason for this rejection is the reliance of classical mathematics on the law of excluded middle, which asserts that for any proposition $p$, either $p$ or not $p$ must be true. Intuitionists argue that this principle is invalid when applied to infinite sets, as we cannot always determine which alternative holds through a finite number of steps.2

For example, while one can decide if two natural numbers are equal, it may be impossible to determine the equality of two real numbers because doing so might require knowing an infinite number of digits. Consequently, intuitionists reject proofs that rely on De Morgan's laws or the axiom of choice when those arguments fail to provide a concrete method for constructing the object whose existence is claimed.23