WARNING: The following article contains spoilers for Star Wars #11, by Charles Soule, Jan Bazaluda, Rachelle Rosenberg, and VC's Clayton Cowles.
C-3PO played an important role in the Skywalker Saga and helped provide some comic relief when needed, but his insults may have been a thinly veiled mask for a darker side. In the movies, he threw snide remarks at Wookiees, humans, Jawas, and many other races, but he took it one step further in Star Wars #11.
The Rebel Alliance had just stolen an ancient translator droid from the Imperial Museum with hopes to create a new code that the Empire could not intercept, which could then be used to bring the Rebels back together. As things stand, the Empire would be aware of the Rebels' attempts to communicate with each other. So in order for the ancient translator droid to reach other Rebels, it had to use Lobot, Lando Calrissian's hybroid friend. This process was slowly killing Lobot, much to Lando's distress. Talky, the ancient droid, knew that he was killing Lobot while trying to reach Starlight Squadron across the galaxy.
After Lando is escorted out of the room, C-3PO is able to make his move on Talky. He announces to the crew that he compiled and learned the Trawak language, which Talky had been using as the unbreakable code. Talky is in disbelief as he finds it impossible that 3PO could learn such an ancient language from the few messages he sent out. 3PO then informs the droid that he is outdated and is not surprised in the slightest that Talky's model was discontinued and powers the droid down, permanently, with a quick button press.
While Threepio does kill the droid, there are some solid reasons behind it. Talky was no longer needed as he learned the language and C-3PO would not rely on Lobot to send the communications, thus saving his life. While this was one of Threepio's more savage moments, he never shied away from bullying and name-calling in the movies.
Most of the time, his insults were hurled R2-D2's way, and we're to believe that Artoo dishes it right back. However, Threepio's side is the only one spoken in English. This can be seen as early as in the opening minutes of A New Hope as C-3PO and R2-D2 escape Tantive IV to Tatooine. "Don't call me a mindless philosopher, you overweight glob of grease!" Threepio shouted at Artoo as they boarded the escape pod. It's fair to say that Artoo called Threepio a mindless philosopher first, so the comeback is well garnered. Threepio's insults are thrown towards R2-D2 as either a comeback or out of fear.
There are plenty of times during the original trilogy when C-3PO throws a quick insult Chewbacca's way. The worst case can be seen in The Empire Strikes Back when he lets loose on Chewie after the Wookiee saves him from the Ugnaughts and puts him back together. Threepio realizes Chewbacca has built him backward and calls him names such as "flea-bitten furball" and "overgrown mop-head." Threepio may also throw some shade towards other species' intelligence and characteristics. He tells Lando that Chewie is "only a Wookiee" after Chewbacca acts in an aggressive manner as if to say that all Wookiees are prone to random fits of rage. He also calls Luke Skywalker "... clever, you know... for a human being," implying that he does not view humans to be on the same wavelength as droids.
While C-3PO has said some pretty disrespectful things on the screen, most are not said in a sinister way. His banter with Artoo is mostly friendly. and it's possible that Artoo is giving it to Threepio much worse through his beeps. He occasionally gets upset over situations and speaks his mind, but it's never in a threatening way. While he did effectively kill a droid, his actions helped save Lobot's life. It is not fair to look at Threepio as being malevolent; the only crime he is guilty of is arrogance.