I'm going to be running a new campaign for my players, with our session 0 starting tomorrow. I was leaning towards the traditional ability score method of generation (roll 4d6, drop the lowest). I am not concerned with the numbers themselves but the problems that random numbers could create.
Now, I've just gotten into a heated discussion with several of my players because I mentioned the possibility of using a point buy or standard array for ability scores. When I mentioned the option of point buy, the argument made was that this would lead towards min-maxing and remove their creative input on how to make their character. Not only is this logically fallacious, but the point buy system prevents min-max by limiting scores to a min of 8 and a max of 15, not to mention the system itself seems designed to inherently limit the ability to min-max by placing a hard cap of 20 on abilities.
The problem I'm having is, if we were to do a point buy or array assignment, it would be entirely for their benefit. They don't seem to understand the social problems created when abilities are completely randomly assigned. Of course, if they're hellbent on rolling for stats and I oppose them, that is also going to create a social problem in the game, since it seems this is an early sign of the adversarial "players vs. DM" attitude.
What I am looking for is a good resolution, or compromise, so that my players don't feel slighted and no one ends up with very high or very low numbers, creating overshadowing or spotlighting issues.
Since some of the answers have taken into account my group's long term friendship, I should clarify that with the exception of two players, we've all known each other and been friends (off and on — this is the first time four of us have been at a table together in at least 5; there's a story there but I won't go into it) for 15 or so years, but we haven't been gaming together throughout that time. We used to jam VTM all the time (8 or more years ago), and I've been running a Pathfinder game with some of them for the past 2.5 years (we used a point buy for that game), but this is actually our first serious foray into D&D proper as a group.