That presupposes that no one had previously had willingness to care for others, and that's nonsense.
One reason epidemics are so devastating is that not enough people flee.
It does nothing of the sort.
Rodney Stark uses all the original sources that were available to show there was a significant difference in how Christians treated others vs the Pagans around them.
It is a matter of percentages. Christian doctrine to love your neighbor as yourself, the example of the good Samaritan, and the exhortation to "love your enemies" are all unusual.
Stoic Philosophers pushed for the brotherhood of man. There is a melding of Stoic and Christian doctrine.
There is no question, however, that Christians taught their adherents to care for and value those outside of Christianity.
That was a very unusual concept in pagan Rome.