Imagine that a crime has just taken place a group of witnesses are asked to describe the suspect in question. In one sentence, they say the following:
From my upcoming book, "Write Horror." Art by me.
As you can see, the perspective of the suspect changes depending on who is being asked. A woman might consider this guy unpresentable while someone with a lot more hair and a shaggy beard might believe him to be well-groomed. In a similar vein, an older man might believe the suspect to be younger, while a teen might rightfully say he was older from her perspective.
Of course, in an actual police procedural, officers would push for more details to get a more fordable picture, but I hope this gives you a good idea of why character perspective is important. Quite simply, your characters are going to view each other differently, and not only is it your job as a writer to understand this, but it also allows your readers to have more character development for each player involved.