Before I even get started, I am a big proponent of defining terms. When someone brings up the concept of min-maxing or accuses someone of min-maxing there is a certain archetype in that persons mind. This archetype is usually of someone that only cares about stats on the character sheet, combat, how to bring the most cheese to the table (by cheese I mean min-maxing everything to the limit of the rules), and is not really interested in roleplaying.
With that being said, there are systems that make min-maxing easier and others harder. Then there are some systems that having a well rounded character is the sweet spot due to the genre, mechanics, style, etc. Though, this discussion commonly comes up in Dungeons and Dragons and all other d20 (especially 2nd edition to 3.x) derived games.
There is also something called efficiency and efficiency is something that is in important in these d20 derived games. To define terms again, by efficiency I mean someone who understands the system, is able to create a character they want and what they want their character to be good at, and enjoys the roleplaying aspect of the game. This is because if your character does not have one or two focuses (usually two is the max before efficiency starts to drop due to MAD and other factors. Commonly these focuses are split between combat/social/exploration) it will tend to be alright in a lot of areas but not really good in anything. This can make things really frustrating for the player when the dice start to hit the table as Lady Luck is a fickle mistress. I am speaking from personal experience and what I have seen at the table.
What really grinds my gears is when people accuse efficient players as min-maxing. I personally find this rude and it makes me feel like the person doing the accusing really does not understand the mechanical implications of the game. Maybe this comes from jealously when other characters are more effective at various aspects and they have to rely on high d20 rolls which are manipulated by Lady Luck. It also comes from frustration as lack of successes on the average.
If a player is struggling with the mechanical aspects of the game they should ask for help from an efficient player.
If a player is going to accuse another player of something, they should be using the right terms.
It definitely helps to understand what experience you want from a game and then how a particular system makes it happen...
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