The principle of the excluded middle, part two

The philosophical objection charges that this argument begs the question, using the law of non-contradiction to prove the law of non-contradiction. It says in effect that it is contradictory to deny the principle of  non-contradiction. But the law of non-contradiction is not used as the basis of the argument.
The direct basis for the law of non-contradiction is its self-evident nature, whereby the predicate is reducible to the subject.