화내다 is showing anger out loud, not just feeling it. -고 chains it with whatever came alongside, and in these lines it usually sits in a run of other reactions: 삐지고 화내고, 웃고 울고 화내고, 정정하고 화내고. Two lines use 갖고 화내다, getting angry over some trivial thing — 이런 것 갖고 화내면 안 돼!, 'don't get mad over something like this'.