I believe that there is at least some learning/cultivation; I’ve seen plenty people becoming nicer over time, and some nice people becoming arseholes. However that is not enough to rule out a potential innate component.
I would say that kindness is an expression (not the only one) of empathy. Some degree of empathy is present in the overwhelming majority of people - barring extreme sociopathic conditions and an absence of mirror neurones. So for most people I would say that it is innate to some extent.
Even in cases where empathy is not present, kindness can be simulated or faked and some people with strong sociopathic conditions have proven to be very good at this when it suits their purposes - so I certainly say something with the appearance of kindness can be learned in one form or another.
It can definitely be cultivated - and I would say that this is one of the major qualities in the whole “two wolves” metaphor or, in classical Greek terms, a virtue to be developed.
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Kindness is a behavior, and therefore it can be cultivated and practiced.
It can be learned but it’s hard.
Basically if you suffer through an event it gives you the ability to empathize with similar people.