How do some humans seemingly naturally have positive or mitigated appraisal of stressful events? Appraisal is how an individual interprets a stressful event or a problem. For recurring problems, I understand that there are neuroanatomical structures that play a role in the appraisal of recurrent problems, problems of a certain type that are encountered frequently. For example, the hippocampus is important in the development of episodic memories, and the amygdala plays a role in fear processing. If we exclude individuals with significant lesions to these areas, we have a population of individuals with these same neuroanatomical structures. However, you can find that some individuals have different appraisals of problems. While these structures are biological intermediaries to cognition, the results are different. How, and why? 

For example, this can have implications in sports. Two players of a professional basketball team could both be the most skilled players on their respective teams with a terrible supporting cast of teammates. One player who views this lack of talent as a challenge could take it upon himself to galvanize his teammates and "carry his team on his back", leading to a successful team performance. However, the other player could view his lack of surrounding talent as a detriment, a crutch, and let frustration contribute to his anxiety, leading to a team's downfall. 

Moreover, appraisal could lead to nonchalant perspectives of certain problems, which leads to stress reduction in some scenarios. Back to the sports analogies. In sports, it is said that an optimal trait of a quality defender is "short term memory" in the sense that if opponents have scored on them, the defender does not let this event contribute to future encounters defending opponents. That is, the defender does not think to him/herself, "I got scored on last time, oh no", which leads to a compounding lack of confidence and eventually, performance. 

A natural psychological explanation could be upbringing or priming, but I can find individuals who grew in stressful environments who can handle stress well, and can't handle stress well. Moreover, I can find individuals who grew in environments where stress was not a significant factor, and again, you can find people who handle stress well and those who don't handle stress well.
The interactions among several factors probably account for variability in reactivity to stressful events, including genetics, epigenetics, early life experience, and culture (e.g., Alexander et al., 2009; Boyce &amp; Ellis, 2005; Francis, Frances, Liu, &amp; Meaney, 2006; Gunthert et al., 2007; Meaney, 2001).  And individual differences are observable at multiple levels of analysis, including behavior, physiology, and brain structure and function.  

On the one hand, there is a huge literature on the development of emotion regulation in children (e.g., positive appraisal of stressful events).  For example, there are models charting the complex influence of the family on emotion regulation development, where parenting practices interact with child characteristics to influence emotion regulation success and strategy use (Morris et al., 2007):



Positive (re)appraisal requires good cognitive control and working memory (McRae et al., 2012), which is associated with functional and structural integrity of cortical areas, most notably prefrontal cortex (Goldsmith, Pollack, &amp; Davidson, 2008; Levesque et al., 2004; Lewis &amp; Stieben, 2004; McRae et al., 2012).  And the ability of PFC to dampen negative affect seems to be mediated by functional connectivity with subcortical areas, notably bilateral amygdala (Banks et al., 2007; Buhle et al., 2014; Wager et al., 2008).  



Positive reappraisal also benefits from practice, which forms part of the basis of cognitive-behavioral therapy (Beck, 2011; Goldin et al., 2012; Goldin et al., 2013).  

Additionally, there is emerging evidence that genes (and gene-environment interactions) are related to emotion regulation strategy use and effectiveness (e.g., 5-HTT, OXTR; Canli &amp; Lesch, 2007; Hariri &amp; Holmes, 2006; Kim et al., 2011).  So genetic factors may promote resilience even in stressful environments. 

Conclusion

So as you can see, there is a large host of factors that contribute to one's tendency to appraise (negatively or positively) a stressful situation. And indeed, you may see large within-person variability in the tendency to make positive appraisals, especially as the context changes (Aldao &amp; Nolen-Hoeksema, 2012). Not to mention, positive appraisal may not always be a beneficial way to mitigate stress, and may instead sometimes be harmful or ineffective (Troy, Shallcross, &amp; Mauss, 2013).