Arguably is the exact opposite of “something is sure and you shouldn’t even discuss it”.
It means, literally, capable of being argued; and if you look closely at your two definitions from dictionary.com you will see that they both support this meaning:
1.susceptible to debate, challenge, or doubt; questionable: Whether this is the best plan of action or not is arguable.
That is, arguments may be advanced on both sides of the question of whether this is the best plan of action.
2.susceptible to being supported by convincing or persuasive argument: Admirers agree that it is arguable he is the finest pianist of his generation.
That is, an argument may be advanced that he is the finest pianist of his generation.
The difference between the two lies in different meanings of the words argue/argument. An argument may represent either
- a) a single proposition or position and the reasons and evidence supporting it; this is the sense employed in definition 2.
- b) the competition between two opposed propositions, each with different reasons and evidence; this is the sense employed in definition 1.
But definition 2 does not support the sense that “something is sure and you shouldn’t even discuss it”. Even the pianist’s admirers do not advance the notion that his status is beyond argument; on the contrary, they say that a good case can be made for his being the finest of his generation.
I am at a loss to account for your dictionary’s offering that meaning. Are you sure it isn’t addressing inarguably or unarguably, which do in fact have that meaning? Neither is used to mean “incapable of being asserted”—an odd asymmetry, but that’s English for you.
Best Answer
The word does have some pejorative cast to it. It is not internet slang; it predates the widespread adoption of the internet (I remember it from ~1980s).
The word exists in contrast to the word "artistic". It often means, when applied to a person, that they have the personal style associated with artists: it suggests that they present themselves -- in speech, dress, habit, activity -- as belonging to a subculture of artists. In an important sense, it functions like calling someone a goth or punk rock or emo: you're saying something of how they seem to you, in terms of subcultural style affiliation.
Perhaps a better definition is that artsy means in the style of artists, where it is understood that there is some artists' style being alluded to. It is in the very differentiation between actually being an artist, and (merely) adopting the style of artists, that the pejorative implication arises.