The 'Liar paradox' makes no sense to me...

The statement “I’m lying” cannot exist on its own; it always necessarily refers to an earlier statement. It’s like the phrase “this is correct” — It cannot exist on its own or else it means nothing. It must refer to something else. When someone says “I’m lying,” they’re usually referring to their previous sentence.

The definition of a ‘liar’ can be either fluid or rigid; it can be someone who lies sometimes (I.e. lied at least once in their lives but can switch back and forth between lies and truth-telling) or someone who always lies (I.e. always lied in the past and cannot ever tell the truth).

Assuming the first definition; if a liar says “I’m lying” then he may or may not be telling the truth in this case (depending on whether his previous statement was objectively true or false)... Whether his statement “I’m lying” is true or false does not matter because a liar by this definition doesn’t have to lie all the time in order to be categorized as such; no contradiction in this case.

If you assume the alternative definition that a "liar" is a person who always lies (is physically incapable of telling the truth and simultaneously retain the ‘liar’ label), then this person would not be physically capable to say "I’m lying" because we just defined a liar as someone who cannot tell the truth... Being a liar means that everything he ever said in the past was a lie (including his previous sentence), therefore, him telling us that he is lying would be the truth... And since, according to this definition, a liar is not capable of ever telling the truth, then he would not be capable of telling us "I’m a liar" because that would be the truth and we just said that a liar cannot do this by definition. He would cease falling under the ‘liar category’ if he told the truth. No contradiction in this case either. Note that as soon as we try to factor ‘free will’ into the discussion, we are inherently accepting the first definition of a liar as someone who only lies sometimes. If he has free will, then surely he can choose to lie or not lie regardless of who he was up to that point.