Here is my spin on why even stuff is bad when animating living things.
Firstly, what do I mean by even? Well its when things seem to have a pattern to them, sync up or move with symmetry. It might be two characters starting to move away on the same frame at the same speed, a blink where the eyes take the same amount of frames to close as they do to open, twinning in a pose is an evenness, or when a character makes several movements that all take about the same amount of frames. I use evenness to describe anything that gives the view a clue that the animation is made by a logical mind, instead of happening spontaneously.
You see the problem is that we are trying to convince people that they are seeing something alive, and as a general rule people (or any living organic thing ) don't move in such a predictable fashion.
When I have taught this in the past it is at about this stage that a\some students will challenge my generalisation. The will say that sometimes people do just happen to move in unison, or in patterns of timing, they might even be able to find an example of someone moving like that.
But there is a problem with relating these examples to your animation. When we see real people, we start from the point of believing they are real, they can move in many different ways and we still believe they are real. We don't stop believing in someone just because they do the robot dance. With animation the tables are turned, people start from the position of knowing it is not real, then we have to use our craft to get them to forget that. We want to eliminate any possible reminders that they are watching something that is made up made, and patterns, symmetry or evenness in your timing is a dead give away.
Of course unreal stuff can happen in your animation, but if so then we want to draw the audience in with a few tricks first so that they come along for the journey. We want our audience to believe in the threats and dilemmas that our characters face, even if the actual actions taking place are beyond the norm. Avoiding evenness id one way of drawing the audience into our made up world.
What we are doing is taking the subtle imperfections within the movement of living things and slightly exaggerating them in order to drive home to our audience that they are watching something alive. So take a moment to consider how organic the movement in your character animation is.