Where to begin? Perhaps we should start with Jiren's design. On the surface, it appears very simplistic and possibly even generic, a passé take on the popular conception of what extraterrestrials may look like. This, of course, is the outlook of those less learned and knowledgeable of Dragon Ball: to create powerful characters with simplistic and and basic designs is Toriyama's hallmark, and, upon closer scrutiny, Jiren's rather unremarkable design perfectly reflects his character: a simple warrior with but one goal--to achieve ultimate strength. He isn't interested in recognition and fanfare; he has no time for flashy transformations and techniques that merely imitate growth. No, it is his personal desire to FACILITATE growth: spiritual growth, physical growth, and intellectual growth. A rather straightforward and simple goal, much like his overall design. Those with genre savvy or a sharp enough intellect could immediately glean various aspects of Jiren's character simply by laying eyes on him.
Too, his color scheme reflects his inner virtues: crimson, symbolizing his passion for and unwavering belief in attaining his goals (and sharing its color with his aura) and black, obviously symbolizing the bottomless void and never-ending journey of bettering oneself--a journey that never truly ends. Even his gray skin--far from simply being a ripoff of the grays that were so popular in the 50s--symbolizes his ultimate neutrality, being itself a neutral color. He's not interested in fame, fortune, conquering, or dominating: like gray symbolizes, Jiren seeks only to achieve his goals without the burden of interpersonal ties or outside distractions.
Now, on to the meat of this fascinating character. At first glance, Jiren seems standoffish, stoic, and perhaps unfriendly and selfish. Upon the revelation of his backstory, we learn that his master and family were killed by a villain that Jiren was powerless to stop. His master--the man who instilled within Jiren his passion for and love of martial arts and the cultivation of pure, inner strength--was taken from him by an evildoer, and in that moment Jiren realized two things. One: Caring about ANYTHING is meaningless without wielding the requisite might to protect it, and two: Living a life unfettered by close emotional ties serves to protect one from pain and minimizes distractions that seeks to deter one in their quest for personal growth.
In layman's terms: Jiren is heavily afflicted with PTSD. His trauma, while it doesn't fully control him, certainly plays a part in his overall nature and how he holds himself. He has formed a group of do-gooders with like-minded individuals, but he isn't close to any of them, nor is he close to any of those he saves beyond the usual "hero-victim" relationship. What appears to be a simple rude and standoffish character is eventually revealed to be yet another aspect of his complex and dual nature--Jiren WANTS to be free from the burden of the past, he WANTS to blindly place faith and trust in his friends and make that a part of his power as Goku does, but he can't. He simply cannot. And this is why he's so angered by the Saiyan's mere presence, as well as the reason behind his attack on the stands upon realizing he was losing their battle. Jiren wasn't lashing out at Goku's friends: he was lashing out at his own insecurities, trying to destroy his past demons in the only way he knows how--by brandishing the immense strength that was, ironically, cultivated as a result of those same demons.