That's the disagreement. There are many drivers on the road that I would assert, when their behavior does finally inevitably land them into a wreck, did so deliberately. Now, I am sure that if you ask them, they would claim that they did not "intend" to get into an accident, but the utterly reckless behavior with which some people choose to operate a ton of steel hurtling down the road at 60+ mph sings a very, very different tune.
(Now, I'd also accept just a simple "car wreck" or "collision", as suggested by a sibling, which doesn't assume that there was wrong doing, at least, unless the facts suggest otherwise.)
It's a result of negligence, impairment of intellectual functioning, or a number of things other than an accident.
The word crash covers such an incident far, far better. (Edit: Collision works as well, having read nearby comments).
For proof, watch any recent Dashcam Owners Australia monthly compilation. Most of these are not accidents.
But accident is a civil term, not a legal term. Legally there's a spectrum of culpability from driver innocence (the brakes failed, the lights failed, a bob cat fell on the windshield) to premeditated murder, with negligence and recklessness in between.
There may still be legal responsibility elsewhere. Did the brakes fail because the garage made a mistake?
Of course you can have an accident because you were reckless. That doesn't mean you wanted to kill someone. It means you were taking avoidable and unnecessary risks and didn't get away with it.
When people engage in reckless endangerment, there's a crime for that: reckless endangerment. When the driving was stupid, but not to the level of criminal, there's a lawsuit for that.
"Accident" also very nicely preserves the assumption of innocence until proven guilty.