But it's a temptation that needs to be resisted, because there simply aren't enough points of commonality
Big wrong there! The commonality is that most, well in excess of 90% (and way higher in the serious violence stakes) violence, the perps are male. Most of the mass killers and serial killers, again male. Most of the DV abusers, male. Most major crime, male. Male, male, male, male.
Of course, the papers will milk any female violence story to the max - they are the exception. But if you count it on actual incidents, not coverage, male violence and criminality is the overwhelming pattern.
But further than that, media coverage will quite often minimise or excuse male violence, and emphasise female violence and denounce the perpetrator.
I am astounded that most people seem blinded to that pattern. Really, it is easy to spot (but patriarchy will shut you up about it).
I tend to agree with PatriarchyPersonified, it is a bit too widespread across time and space to write it off as conditioning. It's a flaw, a fundamental flaw.