Some hindrances I find to truly understanding why abusers abuse:
A. A basic sense of how other living humans perceive the world or have feelings, is in the back of our mind all the time and reflects back to the average person.
If this is how your mind works, then if you were relaxing on a sofa and somebody you lived and had an amicable relationship with walked right into a table corner in your line of sight/hearing—then, the "sensor of other people's feelings" would usually override your physical response: Maybe you'd almost-involuntarily jump up, say, "Oh no! Are you okay?!?" And if you saw their shin scraped bloody from the table corner then you might even scream softly even though it's not your shin. There might be this ghost of a pain in your own shin.
Somebody who lives like this will become challenged in imagining what it's like to watch somebody be hurt, to know that they're hurt, and to not be inclined to alleviate that pain. Or even, what it's like watching somebody in genuine pain and imagine that experience translated, in a different kind of mind, as something fun to watch or to cause…that even if they've been told it's wrong, they'll find ways harm others as much as can be gotten away with. There isn't that internal checkpoint of, "I have to stop because this is hurting me too."
B. The conflict-resolution learning curve. The "sense of other people's feelings" doesn't always work. Some people are limited by having very different life experiences than others.
Somebody who's had wonderfully supportive parents who can talk through every disagreement and in hindsight even getting grounded was good…would not have any sense at all of what it's like for somebody else to have cruel parents. The 'basic sense of other people's feelings' turns into the very worst advice of "But they're your parents, of course they love you, you're the problem for not talking it out"—or in cases of eating disorders and self injury, "just eat!!" or "maybe don't do that fingertip-picking thing, duh" and then it's like 'thanks, I'm cured…not'.
So, just because a person can scream at somebody else's bloodied shin doesn't mean that they cannot or have not committed an abusive action against somebody else out of ignorance with life experience or lack of understanding.
But usually, when reasoning or life experience gets through, there's this sense of guilt or embarrassment and wanting to admit to that wrong to clear one's own conscience—and do better next time, repair the harm if they can.
Some abusive people act out of genuine ignorance and obliviousness or callousness…and, others are more willful about the same thing, constructing these logical acrobatics (really, logical fallacies) to refuse to recognize or admit that they were flawed or wrong or that they hurt somebody.
C. Control, imposition, and lack of boundaries
Sometimes it's compensatory—Abuse victims, especially those victimized in childhood, very often grow up to be abusers because they internalized this idea that if absolutely everything is not absolutely perfect all the time, then they're not safe and they will be hurt again.
In these cases, everything mentioned in the Duluth wheel stems from that: An abusive person is highly motivated to control somebody else's financial freedom, because somebody else having a different perspective of their own or a empowered to do unpredictable things is genuinely upsetting to some kinds of abusive people. So, whether it's planned or ruminated or improvised…there's a persistent imposition from an abusive person onto their targets, not only financial autonomy but everything else, social support system, eating habits, self-expression, sleep schedule—everything imposed according to the abusive person's overly compensatory satisfaction. And, because the root of this is an emotion or a habit that is not appropriate to the present situation, there's pretty much never going to be satisfaction.
There's not going to be this sense of "I've felt safe for long enough that I can calm down, perceive the world clearly enough to recognize that I have treated others badly, and improve my behavior or make restitution."
There isn't this sense of "not everything has to be under my complete control", because the desire for power over the victim or victims often comes from an emotional need for safety.
D. Inconsistency. The Cycle of Abuse makes it look predictable: Many abusers will behave very nicely, and then they'll be abusive, and then they'll be nice again.
It's difficult to explain the difference between a person with a strong moral code who was in a bad situation and did something they know is wrong, goes into a depression due to the "moral injury", then has to try to find a way to forgive themselves and move on with their life—or somebody learning what their moral code even is—versus somebody who claims to have all these values and then behaves very hypocritically.
I think there's this tendency to think of abusers as more conscientious than they actually are, like some conspiratorial villain from a Shakespeare stageplay who monologues their motivations and analyzes and plans.
Otherwise, why can many real-life abusers control their temper in front of a law enforcer, or in front of somebody that they're trying to impress or to use/manipulate; or somebody I used to know would "prefer" talking things out rather than text or email—just so that she could say later, 'I never said that' when she did.
Most times I really think it's as short-term in thinking as… it's what's worked for them, that they can get away with. Maybe they fall into habitual, not at all right, ways of dealing with whatever their deal is.
But the thing about behaving inconsistently is that, usually, victims will want to continue believing that the "honeymoon" phase in the Cycle of Violence model—the best face that person shows—is what that abusive person is truly like at heart, whereas the abusive episodes are conditional and temporary: "he's had a bad day and isn't always like this", "she's had a rough childhood and is working through it", "I can love them enough to change them and we'll never have these problems ever again", those kinds of excuses.
I think that usually it's the other way around, that the "best face" is the temporary conditional thing, instinctively going into that mode only to get by in society—but the motivations for abuse, whether that's sadism or perfectionism or fear or obliviousness or stubbornness, remain more central to what that abusive person…needs to recover from, but heaps that pain on others for temporary relief instead.