Actually we are far less physically aggressive than other primates. A theory I can suggest:
It has been well documented through primate research that primates will only physically attack an opponent if they have a significant advantage over them (size, strength, numbers). You will rarely find less than 3 chimps attacking 1 opponent chimp - they need the advantage to attack, and if they don't have it they won't. The same occurs with humans, but the variance in size and strength is small between us so there are rarely opportunities to get that advantage. I'd assume verbal attacks are resorted to because it's a way to be aggressive with a small chance of physical retaliation - so you get a net positive in aggression vs risk. Finding those chances to attack with a significant advantage are rare, especially since altruistic individuals in society will step in and help stop it.
The more likely answer is not evolutionary/biological at all though. It's simply that we have laws that punish physical assault and protect free speech. Naturally people find the risk/reward of verbal attacks better than physical because of these laws.
I'd also say that verbal aggression has become integrated within society (social media, text messaging etc) and has created a norm for verbal aggression. Afaik we've seen a fall in physical aggression and rise in verbal since the digitalisation of society.