I'm just wondering property about validity of argument so I made this weird argument. But it seems that I still do not understand these things...
Suppose that An argument must be either valid or invalid but not both simultaneously(this is easy to accept), and
Argument Ⅰ:= If argument Ⅰ is valid, then argument Ⅰ is invalid.
Then we can rewrite argument Ⅰ as [‘argument Ⅰ is valid’ ⇒ ‘argument Ⅰ is invalid’] ---- α
Let’s check the validity of this argument.
(1)Suppose that the proposition ‘argument Ⅰ is valid’ (hypothesis of Argument Ⅰ) is true. That means that when the proposition ‘argument Ⅰ is valid’ is true, the truth value of the proposition ‘argument Ⅰ is invalid’ is true. (see α)
(2)Besides we supposed that the proposition ‘argument Ⅰ is valid’ is true, so the truth value of the proposition ‘argument Ⅰ is invalid’ also becomes true by (1)
Hence we can conclude that the conclusion of the argument is true if the hypothesis of the argument is true. In other words, the argument Ⅰ is valid.
This conclusion seems very weird because we just said that if the argument Ⅰ is valid, then the argument Ⅰ is invalid. This result seems to represent an infinite regression.
Also, another weird point appears when we find a valid argument Ⅱ by
Argument Ⅱ:= If the argument Ⅰ is invalid, then the argument Ⅰ is valid
(∵ Suppose that argument Ⅰ is invalid, which means that if ‘argument Ⅰ is valid’ is true, then ‘argument Ⅰ is invalid’ is false. We can represent this as argument Ⅰ is invalid if and only if, if argument Ⅰ is valid, then argument Ⅰ is valid (i.e. ‘the argument Ⅰ is invalid’ ⇔ ‘If the argument Ⅰ is valid, then the argument Ⅰ is valid’).
Hence we can make a statement as [‘the argument Ⅰ is invalid’ → ‘the argument Ⅰ is valid’] ⇔[‘If the argument Ⅰ is valid, then the argument Ⅰ is valid’ → ‘the argument Ⅰ is valid’] ⇔[‘the argument Ⅰ is valid’ → ‘the argument Ⅰ is valid’ → ‘the argument Ⅰ is valid’] which is obviously tautology)
Therefore we can say that “if the argument Ⅰ is valid, then the argument Ⅰ is invalid” by valid argument Ⅰ and “if the argument Ⅰ is invalid, then the argument Ⅰ is valid” by valid argument Ⅱ. In other words, we proved that [‘the argument Ⅰ is valid’ ⇔ ‘the argument Ⅰ is invalid’].
You haven't defined what an "argument" is or what a "valid argument" and without rigorous definitions who is to say whether the "easy to accept" statement that every argument is either valid or invalid is meaningful, never mind true. Your reasoning is a form of the liar paradox. There is a vast (IMHO far too vast) literature on such paradoxes.