If the statement is true, everything asserted in it must be true. However, because the statement asserts that it is itself false, it must be false. So the hypothesis that it is true leads to the contradiction that it is false. Yet the sentence cannot be false for that hypothesis also leads to contradiction. If the statement is false, then what it says about itself is not true. It says that it is false, so that must not be true. Hence, it is true. Under either hypothesis, the statement is both true and false.
I.e consistent within the confines of the axioms and contradictory outside the confines of the axioms. So it is both inconsistent and contradictory, while at the same time being consistent in logic or semantics we have a paradox.
The Liar Paradox does not exist. To say "I am lying" is to say "I was lying when I said the thing I just claimed previous to this statement." The Liar does not mean "I am lying when I say this very statement." Such a statement is not even subject to true/false evaluations.