Every concept is contradictory to all other concepts.

You can show the line of reasoning is fallacious if you can give one counterexample. To some extent we are hindered by the phrasing of the question. But suppose the concept of democracy is realised in America because it is a country that plans to hold an election on 3rd November 2020. And suppose the concept of car is realised when one of the contestants tours past crowds in a limousine. Then if said tour took place in said country I think you have an adequate counterexample.

I agree, sounds more like a wanna-be absurd extrapolation.

There's a difference between the model and the reality; they are not the same and should not be confused for one another.

In reality, it is often possible to have somewhat contradicting systems in place and societies cannot always be neatly divided into fine, exclusive categories, like "democratic" and "non-democratic." Thus, you can have 'car' in democracy, since 'car' is not 'democracy', but exists alongside it. 'Green' is a colour, but that colour can exist inside a democracy, because the concept of colour transcends politics in the first place.

This is a) someone being pretentious and b) probably reification.

EDIT: I'm also not fully sure what this person is trying to suggest here - that we don't live in a democracy?

Hi, sing!  
   
            You say, “I feel that, if they are distinct, it doesn't mean that they are contradictory.” I agree, sing. Let me try to put arguments to your feelings.   
   
            The unnamed person in your post is making identity claims: the person is saying that the concept democracy and the concept green, for example, are not the same concept. She is right, so far. The concept democracy is not the concept green, nor is it the concept car. However, she is mistaken in concluding that the two concepts are, therefore, contradictory (indeed, that the one concept contradicts every other concept.)   
   
            The claim that x and y are not identical does not entail the claim that x and y are contradictory. Identity claims can be properly made about things that are not propositions, whereas claims about contradictions can be properly made only about things that are propositions. For instance, it can be said that I am not identical to this water bottle. But it would be improper to say that I contradict this water bottle. This is because I am not a proposition (neither is the water bottle). Since it is true that I am not identical to the water bottle, but false that I contradict the water bottle, it follows that “x and y are not identical” does not entail “x and y are contradictory”.  
 
            I consider the above argument to be the weaker of the two that I have to offer, but below is a reinforcing argument whose basic format can be used to rebut certain potential objections to the above argument. 
   
            Even if x and y are both propositions, the claim that x and y are not identical still does not entail the claim that x and y contradict. Is the proposition I have two arms identical to the proposition I have two legs ? No. But are they contradictory? No; it is possible that both are true. Therefore, to say that x and y are not identical does not entail that x and y contradict, even if x and y are both propositions.  
   
   
Thank you, sing.   
   
From, Kaiden

Are you quoting someone in particular or is this just a thought experiment or something else? This came to mind as an answer. I use the quote rather than try and funnel complex philosophical issues and terms through my own voice and butcher the idea and terms in the process.  

“The twin foundations of Aristotle's logic are the law of non-contradiction (LNC) (also known as the law of contradiction, LC) and the law of excluded middle (LEM). In Metaphysics Book Γ, LNC—“the most certain of all principles”—is defined as follows:

It is impossible that the same thing can at the same time both belong and not belong to the same object and in the same respect, and all other specifications that might be made, let them be added to meet local objections (1005b19–23).”

Stanford Encyclopedia of Philosophy 

Thank you very much for every reply. I guess that it runs as follows.

1) not-a is a contradiction of a.

2) everything, except a, is not-a.

3) so everything is a contradiction of a.

It seems to be correct but my sense tells me there should be something wrong.