Whats analysis of both sides is called in psychology? What is the scientific term or psychological term for visualizing a phenomenon, news or event in history or in daily life from both perspective. For example some event that happened in your country or a war your country fought, the basic sentiment of most people will be in support of their country or military but if you want to put forward a case both in favor and against of that war without following the general emotional consensus in your country what that would be called?
As highlighted in the comments, not all observations necessarily need a term in psychology, but there is a term for this.

Therapy plans will often involve getting the client to try to look at their situation (past or present) in a different context. Some people would call this "wearing other peoples shoes", or in other words they might say "if I were in their shoes...", and some will call it looking at it from another person's viewpoint or perspective.

The more accepted term you are after is Emotional Intelligence (Bertram, et al.  2016), also known as Emotional quotient (EQ) and Emotional Intelligence Quotient (EIQ), yet I dislike the terms involving intelligence because it insinuates that those who find difficulty with looking at certain people's points of view are not as intelligent as others who can.  Yet this is not necessarily the case.

Emotional Intelligence involves the capability of individuals to recognize their own emotions and those of others, discern between different feelings and label them appropriately, use emotional information to guide thinking and behaviour, and manage and/or adjust emotions to adapt to environments or achieve one's goal(s) (Coleman, 2008),
 and Jeremy E. Sherman, PhD. calls it Empathic Intelligence (Sherman, 2009).

References

Bertram K., Randazzo J., Alabi N., Levenson J., Doucette J. T., &amp; Barbosa, P. (2016). Strong correlations between empathy, emotional intelligence, and personality traits among podiatric medical students: A cross-sectional study. Education for Health, (29)3, 186. DOI: 10.4103/1357-6283.204224, PMID 28406102

Colman, Andrew (2008). A Dictionary of Psychology (3 ed.). Oxford University Press.DOI: 10.1093/acref/9780199534067.001.0001

Sherman, J. (2009). Empathic Intelligence: To put yourself in their shoes, unlace yours. PsychologyToday [Online]Retrieved from: https://www.psychologytoday.com/us/blog/ambigamy/200905/empathic-intelligence-put-yourself-in-their-shoes-unlace-yours