Concept fallacy?

I encountered this argument about democracy and political correctness, and it went something like this:

P1: Democracy is based entirely on freedom of speech.
P2: Political Correctness suppresses freedom of speech.
C1: Therefore, Political Correctness has destroyed and replaced democracy!

I feel there is a logical fallacy in this argument, but I dunno which one.

An additional one I found is also this one, about the controversial Serena comic:

P1: Political comics on newspapers often exaggerate features, and it happens often.
P2: This comic that features racially charged characteristics on Serena is also exaggerated.
C1: Therefore, this racially charged comic is not racist, because it happens to everyone.

Generally speaking, you are dealing with non-sequiturs . Let's look at a VALID (truth of the premises guarantees the truth of the conclusion) version of this argument:

P1: A properly functioning democracy requires unsuppressed on freedom of speech.
P2: Political Correctness suppresses freedom of speech.
C1: Therefore, Political Correctness is a cause of a democracy that is not properly functioning.

Now let's look at this fallacious version:

P1: Democracy is based entirely on freedom of speech.
P2: Political Correctness suppresses freedom of speech.
C1: Therefore, Political Correctness has destroyed and replaced democracy!

The wording makes the conclusion incompatible with the premises, because there there is no connection between "based entirely," "suppresses," and "destroyed and replaced" so the conclusion simply does not follow. What I did in the valid version is massaged the language so not only does the conclusion follow, but the conclusion is guaranteed IF the premises are true. The other argument you posted was similar.