A neutral alignment would be about avoiding both good and evil choices, not about doing a balanced number of both. As a DM, I would generally consider the latter simply evil with the desire to not appear evil to either oneself or others - either deceitful or delusional.

I'm basically echoing LadyLorraine here, but the reason neutral alignments aren't encouraged is because while good alignments try to change things things for the better for everyone, and evil alignments tend to change things for the profit of the individual (or for the worst for everyone, in the case of the more fantastical evils) neutral alignments generally avoid change and attempt to maintain the status quo. That's pretty much the anti-narrative. Nobody wants to read a story about some guy who left his village in order to stay the same.

The other possibility is alignments that are not in concordance with the predominant good/evil axis. Essentially, these are people who would consider themselves good but have a definition of good/evil very different from the dominant theme, without their actions being clearly defined by good and evil. Essentially, this is your character who actually does perform good and evil actions in balance, but it's not with the goal of actually staying in that balance, but rather with the goal of achieving what is good in their own moral system.

The first example I can think of for something like that is the old D&D Druids, who were all about nature. This isn't the neo-elfin vegetarian eco-terrorist nurturing nature, mind you. Nature's actually ridiculously vicious. As an example of active good, Druidic-neutral and evil alignments, imagine some shepherds have been losing sheep to wolves, and one of the shepherds actually got pretty severely injured trying to drive them off. Now, say, a Paladin might lead a hunt to track down the wolves and keep the shepherds safe. An evil character would probably not care, but might do the same if he were paid. And the Druid would probably consider this normal struggle for survival - the wolves try to hunt the sheep to feed, the shepherds try to drive them off to keep their livestock, and therefore their livelihood intact. Sometimes one wins, sometimes the other. This is as it should be. If anything, he would consider an attempt to hunt down the wolves an aberration, something akin to genocide, and probably try to stop that.