Im not confusing anything.
Yes you are.
What exactly do you think a per capita homicide rate is measuring/representing in the overall population, and why would it be important to equalize it across cities with different populations?
The answer is that a per capita homicide rate is measuring an estimation of the individual risk of being murdered in each city, and providing equalized scale to that data point so that different cities can be compared in a statistically sound way. That's where face validity exists for a per capita-adjusted homicide rate.
There's nothing wrong with doing that, but that's not what I'm discussing.
What I'm discussing is the question of which cities have the biggest "murderer" or "rapist" problem. Standardizing such a statistic is unsound because by doing so you're intentionally equalizing the quantitative measure you're assessing for differences.
Are one's chances of becoming a homicide victim typically going to become smaller as a N becomes larger? Of course. But that's not the same thing as saying that one large city has a much bigger problem with murderers than a small city who has far fewer murderers and dead bodies.
Watered-down averages have a tendency to do this, especially on a state or national scale. It's why things like overall IQ score are relatively meaningless. It's why average income, gas prices, home prices, etc. are relatively useless, because on an individual basis, you're going to get a much better read on the impact of individuals if you're NOT using overgeneralized averages.
Hiding the absolute value of a raw number such as "total murder victims" by using overgeneralized averages and conflating "the risk of becoming a murder victim" with measures that show an absolute value of murderers in totality is a definitive form of misleading statistics.
We're not trying to become average at the number of murder and assault victims we have--we're trying to eliminate them altogether. This is another reason why it makes no sense to standardize populations in order to gauge risk of victimhood in the context of assessing the problematic elements of violence in a city. "Deviating to the mean" is not an appropriate concept in the context of assessing total murder victims in any given city.