How should a tutorial teach matchups or fundamentals?
By explaining the tools that the character you're versing/looking at has? Blazblue has done a sort of thing with explaining the basics and idea of how to play each character since Continuum Shift 1/2.
I get what Himu's getting at: SF4 is
awful to new players. It doesn't explain ANYTHING to them and just throws them into the deep end. Himu's comment on the training mode is apt. How the hell is a new player going to use that stuff if they don't
understand the basics?
Himu's entire opposition is basically to take the old infamous SRK essay quote: "You can take a SF scrub (read: old-school players) but can't make them think (read: see where fighting games have gone/evolved/improved)." SF has 20+ years of "emotional" baggage. If someone so much as suggests having a basic (BASIC) tutorial mode that explains the systems and beginner level stuff (move forward/back, etc. Yes, this is "awful" but needed to get people into it) you get a lot of opposition from the arcade oldbies that think people should be beaten to death in an attempt to make them sink or swim.
Case in point:
I hope they put in a good tutorial mode Virtua fighter and tekken tag 2 style in SFV. If they don't 
There's already one in SF4-- it's called going online and learning shit.

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That's not to say that Morma and Bork's logic of "tutorials won't make a player better" isn't valid, but to say that SF shouldn't get a tutorial to help newer players "get a grip" on the series conventions and shit would be pigheaded, IMO.
Though really, the problem with that old-school method is that fighting game terms have sooooo many different names depending on series for the same shit at times that it's hard for new players to try out multiple series to see what they want when they're being told "overhead, stuffed, meaty, okamezi, oumi, etc." and going "huh?" iplaywinner's glossary helps, but the lack of "standard fighting game terms" like a sort of "metric" base-line also hinders the genre from having people pick it up. (IMO)
SF4 relied on the training mode's recording function for that sort of practice, which obviously necessitates outside research. The closest they came to the above was the challenge mode, but as the name suggests, that's more of an input olympics thing than it is proper training. Maybe they couldn't allocate any resources for that, who knows. Or they knew the community would pick up the slack, so they didn't bother.
Baseline SF4 is an excellent fighting game, but the negative quirks are pretty bad. Worse matchmaking system I've seen in any console game, the ping meter doesn't mean shit and it takes up to a minute to find a ranked match. Mainly because of getting disconnected by someone joining at the same time. The non ranked match options are sparse as fuck. I'd guess more resources went into adding characters than anything else.
A lot of people thought Dead or Alive 4 was meh, but it had the best and most robust room hosting for a fighter.
But had worse Netcode than DOA2U. DOA2U's netcode was the best of a 3D fighter (or even a fighting game in general) ever. Slowing the game down when the connection lags so both players can hold/parry a move.
The luchador is the most fucked character to play online. People that are in the top 100 as him should be fought by jumping and kicking erratically. He may be a joke when it comes to characterization, but he's the scariest character to fight.
Playing fighting games online. Now,

right? Especially 2D.

(And yes, I know I'm a hypocrite for mentioning DOA2U online. But you seriously can't translate online skills to offline. Wayyy too much lag tactic bullshit that won't stick in zero-lag environments.)