I prefer rolling dice because I think it's more fun to "discover" a character, rather than having a personality tailored for particular gaming goals. As an old-time gamer, I find it gets my creative juices flowing more to roll the abilities and then consider "what is this guy's personality like?" -- I come up with characters I never would have if I'd just sat down with a blank sheet of paper.
It also makes character generation quicker, and allows for character-development in-game and not fully formed in advance by essay-writing. And that means it's less of a blow to lose the PC to in-game death, which makes the game more adventurous and generally free-wheeling.
Furthermore, I actively dislike how point-buy "irons out" all characters to the same power level -- most interesting fantasy stories don't portray that, and some of my most interesting past D&D campaigns were interesting precisely because they had one character with monstrous abilities, and other PCs who had to take that into account.
Finally, keep in mind that ability rolling is also more inviting to
new players, because then they don't have to engage in an ability-score analysis prior to playing. They can roll their scores and then learn what they mean through play. It's another example of how advancing ever-more-detailed character-creation options are envied by hard-core players (such as visit ENWorld), but seem to present a barrier to new players entering the game.
As usual, I'm fully aware that most modern hard-core players don't see things the same way.
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An analysis of probabilities behind 4d6-drop-one rolls:
www.superdan.net/dndmisc/4d6curve.html
Gaiden's varying-number-of-dice technique looks a lot like an offshoot from the AD&D 1st Ed. Ability Generation Method V from
Unearthed Arcana (p. 74).