what i mean when i say 'anger is addictive' is more like 'anger can become a bad coping strategy'. being righteously angry feels good. it feels very good to reaffirm your beliefs and fight for them and to stand up for a cause.
however that anger and fire needs to be directed and used appropriately. if you have it take over your entire life, you're going to end up screwing yourself. i'm not saying all anger is bad - anger is good and useful - but you gotta be careful with it.
more immediately, if you use getting angry as a coping strategy, it's one that's almost always going to end badly. if getting angry at something is your comfort food, you're reinforcing those habits of "i feel bad, i have to go be angry at someone to feel better". eventually that takes over your mode of communicating with most people. and your friends will wander off, because they want to be friends with you, not punching bags you unload on.
but, you'll still have that habit: "i feel bad, i have to go be angry at someone to feel better".
and when everyone else leaves you, guess who is going to be the only one you'll have handy to be mad at? yep, it's you.
you end up handing self-loathing and self-hatred an all you can eat protein shake buffet to become bigger and tougher and ready to pummel the absolute ever-loving hell of you.
and, well, that's not a good coping strategy, if that's what it ends up doing, right?