Asuna-Kirito

I believe that's the flaw of the light novel itself. The light novel clearly established the history of Yuuki Asuna and why Kirito was "essential" in "saving" her. I'll give the SparkNotes version of the SparkNotes, Asuna was reared to be the archetype of perfection [her father's the CEO of RCT]. She has a brother, who works for her father; SAO was originally purchased by her brother, but due to a sudden business matter, he had to leave -- Asuna, curiously stumbled upon the game in the living room, and was subsequently "stuck" in it. She spent her early days in a state that almost parallels with Sachi's -- she hid in the inns, and constantly cried. She never played a MMORPG prior to SAO, and more than that, there was the possibility of death. She was more worried about disappointing her teachers in that her homework would be late than in actually being stuck in the game itself. Nevertheless, this "lame" state continued for a while. After a while, she began to go for an "all or nothing" approach -- she essentially went "If I'm going to die in SAO, I'm going to do it on my terms"; she went "gung-ho" on fighting. She memorized the rudiments of SAO from an in-game manual [keep in mind, she is an academic, rote or not]. She went into the fields, and quickly proliferated in levels; but, as a side effect, she seldom slept, she didn't hold any comforts, and she bought the cheapest of sustenance.

Enter Kirito [and much of Aria, which should have covered this], an aberration in the game that is SAO; he's extremely carefree -- it's nighttime, Kirito's stargazing while Asuna taking a small break before resuming her training. I'll skip the subsequent exchanges and focus on the primary picture; Kirito did a lot of "small" things that were meaningful to Asuna [I'd really need to refer to a blog post, or to the light novel for this section; my memory's a little foggy on the idiosyncrasies]. Nevertheless, in a cliche, trite saying, Kirito taught Asuna to actually enjoy life, rather than experience it. Compare the Asuna who owns her own house, cooks her own food, and has a wardrobe with the Asuna that camps out in the fields [which is dangerous; there's a certain ambiguity with what players could do outside of safe zones] and consumes the simplest of meals. Kirito in a way, gave Asuna "life"; she transformed from the servile academic wanting to please, to someone a little more independent, driven by what she wants, and not what her father wants. This essentially served as the "basis" for their symbiotic exchanges -- Kirito helped Asuna realize that life is precious, and not to be thrown away [by hardcore leveling, which would have resulted in an inevitable death], and Asuna helped Kirito realize that he was not at fault [Kirito was a scarred kid, the light novel really didn't cover much of his pain -- there were also numerous time skips, that were attenuated by the subtle indications of them. [It's a little difficult to truly imagine that they were in the game for two years, not two months; they matured, Kirito turned 16 in the game, he entered at fourteen, and Asuna, fifteen to seventeen. They literally matured in SAO].

SAO's always been "good" at adapting the superficial stuff [action, combat, blatant actions], but the nuances in the character that the LN presented is seldom found. I personally keep a cumulative "summary" of what the adaptation missed [episodically] on my blog.