Darklink401 hit the nail on the head; when most people claim that Smash is not a fighting game, they mean that it is not a traditional fighting game. The fighting game community in general tends to be fairly elitist. I am not necessarily implying that that is a bad thing either, but many are defensive about their own game as they feel an overwhelming sense of pride towards their craft and sometimes that means they are offensive towards another. Smash is an easy target as it is an entirely different landscape and there is not a vast amount of player overlap. A lot of Marvel players also play Street Fighter or Mortal Kombat players play Injustice, a lot of Injustice players dabble into Killer Instinct, so on and so forth. Most Smash players are interested in Smash and therefore they are not interested in any of the aforementioned titles; thus, making it a feasible target of hate. Think about Smash as the Justin Beiber of fighting games, he is perceived as less masculine and people will assert that his music is not really music despite the notion that his music is music by definition. In their subjective opinion, it is the truth; however, that does not mean that it is true either. Smash has a huge casual following and usually fighting games do not have that luxury, so there could be jealousy to an extent or, again, elitism as their game is not littered by "filthy casuals." As a member of Test Your Might, the Mortal Kombat forum, I can say with confidence that the game got a lot of the same misguided hate for the same reasons.
Tl;dr: Haters gonna hate.