That's not all of CN. And CN, LN and Evil people can and do have friends.
Yeah, they can and do have friends, but they are the vast exception rather than the rule.
If alignment is a spectrum from Lawful(I like groups, I hate being alone, I think people working together with rules helps the world) to Neutral(I don't care if I'm in a group or not, I think it doesn't matter if you are alone or with a group) to....Chaotic(I hate groups, I want to be alone, I think people working together is a bad idea and fails, only individuals working by themselves succeed).
People tend to mistake Chaotic for Neutral. As long as Neutral is the middle ground between extremes, Chaotic has to mean something that isn't "I can do what I want".
Evil people can, of course, have friends. CE, not so much. Given that it's the Law/Chaos axis that determines your methodology in terms of working as a group.
Not having friends is more a mark of certain character flaws and or having low charisma or other low mental ability scores as opposed to anything to do with alignment.
It's not just that. As people have pointed out, not everyone is a paramour of their alignment. Not all CN people have 0 friends. But most of them have very few friends. And almost none of them are good friends. They are loners by nature. Sometimes that means they tolerate being in small groups with a loose organization.
But they have problems with rules and authority(they aren't just ambivalent towards them, that's Neutral). So they hate being told to do anything by other people. Obviously, not all of them being paramours of their alignment, some tolerate authority and rules(like let's split the treasure evenly, your watch is 2 hours then wake the next person up, please don't run ahead of the rest of the party, etc). However, their alignment predisposes them to break rules just because they are rules. After all, that increases Chaos. You can't be too predictable, that's orderly.
I'd go as far as to say that CN being anarchists at heart that one that WAS a paragon of his alignment would instead do things like randomly determine their actions in combat, randomly determine which side to help out each time there is a combat, and even randomly decide whether they will be adventuring with the party each day. They would actively tear down governments simply because they don't like the idea of anyone being in charge of anyone. They would flaunt laws not for any reason other than they have to act contrary to the rules.
Most people who play CN are actually playing TN. They work much better with other people.
CN is also not about being a jerk either. Anybody can be a jerk, especially LG people.
I think that in an adventuring party, working together tends to be praised more than breaking rules and looking out for yourself. So, although anyone can be a jerk as a personality trait, simply following your alignment correctly as CN ends up being a jerk.
The problem is that the paramour of CN is so horrendously jerky, that each person who plays CN is determining how BIG of a jerk they want to be.