In volume 1, Kirito and Asuna is the clear cut pairing to any reader, as there are no mentions of other girls in Kirito's life except mentioning that he has a sister, without going into detail about her. As nhahtdh explains in his answer, it is very clear that Asuna is the main heroine of the story, and that Kirito is committed to her.
So why are there so many other girls involved with Kirito?
Starting in volume 2, Silica, Lisbeth, Yui, and Sachi, were all side characters introduced to give readers the same feelings that the author, Reki Kawahara, felt when he played MMOs. As with most MMO players, he was never part of one of the top groups, and had great respect for players that could clear the hardest content or had the best items. This sense of awe that was instilled in him in games is the same feeling that he wanted to portray by showing some weaker characters and their struggles and then having a hero show up and really show them how badass someone end-game could be.
Kawahara notes at the end of the volume 2:
I have previously also played some online games. But no matter in what
game, I have never been part of a high-ranking group. I merely envied those
eternally strong players with the best equipment and reputation, one after
another easily defeating monsters, and afterwards feeling that they were "So skilled! So strong!" (haha)
Therefore, I wanted to write about not only the volume one's protagonists
Kirito and Asuna and their type of top players, but wanted
even more to write something about the stories of ordinary mid-level
players; and this second volume's four short stories, have precisely this kind
of content. Regardless of which story, they are basically about Kirito
debuting and causing a big stir; and feeling that he is "So skilled! So
strong!" like Scilica and Lizbet felt, is precisely what I have felt every year
since becoming an MMO player. Really, and once would be enough, I
really want to know what it feels like to show off to others a weapon of
which there are only three copies in the entire server.
Kawahara created many side stories which introduced these different female characters, all of which had their own backstories and troubles to be solved.
However, despite creating these girls and their problems, he always has one solution to their problems: Kirito. Since Kirito is the main protagonist of the story, Kirito was always the hero which would show up to fill this role of legendary MMO player. Kirito is the game's hero and all of the focus and glory shines on him and his perspective.
Additional comments on this matter by Kawahara in volume 2 Author Notes:
Besides that, there's one more thing that I must apologize to everyone about.
Even though the four female characters in this book are all different female
players, their male counterpart, as discussed earlier, was always Kirito-san.
Even though there is no way for me to explain myself to everyone properly
on this point, I painfully excuse myself, and ask that everyone please use
the "even though the criminal and victim change every time, the detective is
always the same person" mindset you have when reading detective novel
series... you can't do it right? Sorry, sorry.