While killing deer temporarily reduces the number, populations quickly bounce back, and culls can actually increase the population long-term. Why?
Remaining deer compensate with higher birth & survival rates
When there are fewer deer living in the same habitat, there is more food for the remaining deer. So when deer herds are culled without reducing their resources, the remaining does birth more fawns, are more likely to have twins and triplets, and those fawns have a higher survival rate (Richter & Labisky, 1985). These fawns are also more likely to have an earlier onset of sexual maturity, as early as 1 year old.
This "compensatory rebound" effect is evolutionary; when there's a sudden decrease in the population, species survival kicks in to induce a high reproductive rate. In fact, those who promote deer habitats for hunting purposes know this, and use it to their advantage when wanting to increase the population of deer for hunters (Deer Density, Buck to Doe Ratio, and Harvest Rates):
"The general theory of harvesting animals is based on the premise that when animals are not harvested at all, growth and recruitment are balanced by natural mortality and that the average growth rate of a population at its carrying capacity is zero. Harvesting reduces the population size, but the reduction results in an increase in the growth rate of the population. This increase in growth rate is brought about because of higher birth rates and lower death rates resulting from decreased competition for resources. This increased growth rate provides a surplus of individuals above the number required to replace the population, and this surplus can be harvested." William Robinson, Wildlife Ecology and Management
Many more studies documenting the compensatory rebound effect can be found here.
Killing never stops; culls must be repeated again and again
As cities who have done culls have shown, the killing
doesn't stop. It is never "one and done"; one of the nation's
largest culling contractors says culls should be done
"like mowing a lawn." Culling must be done year-after-year;
Jackson is on their 9th year of culling deer.
After 17 years of deer culling, the city of Stevens Point, WI
determined the deer population was "roughly the same
as it was." Is this the kind of "solution" we want?
The vaccuum effect
Nature abhors a vaccuum. When a resource-rich area becomes vacant due to a reduced deer population following a cull, some deer migrate in from adjacent lands to take advantage of those resources. Though typically the migratory pattern of deer is limited, when challenged for food -- or when threatened by predator sharpshooters -- deer will travel to find food and shelter in other areas. This is one reason we have more deer in urban areas today. See more information on the vacuum effect on wildlife here.
In our own Barton Hills, deer congregated in open space. But when they started culling in those spaces, the deer stayed away from those areas -- moving into others. If we kill in parks and public places, where will the deer seek refuge?
Deer are highly adaptable (older deer have learned to look both ways before crossing the street!). And just as our neighborhoods have provided refuge from hunters, so, too, will our backyards provide refuge for those deer fleeing the culling in our public spaces. Certain plants are irresistable to deer; even by bringing the deer population down, remaining and fleeing deer will seek out their top-choice plants to eat. Culls could make neighborhood problems worse.
Every year of culling costs more
In a paper entitled, "Adaptive Management of Urban Deer," Nielsen et. al, show that the effort to cull is dramatically increased as the population is a smaller percentage of the carrying capacity. The further we are below carrying capacity, the greater the number of effort (i.e., tax payer money) it will require to conduct a culling operation.
Why culls don't work
Graph from DeerFriendly