This is a crucial scene in the emotional and moral texture of the play, and also a very funny one. The sight of Dr. Stockmann losing his patience so thoroughly at the insulting insinuations of Hovstad and Aslaksen that he menaces the latter with an umbrella gives a refreshingly human touch to his righteous indignation. This physical manifestation of the doctor's rage is absent from Arthur Miller's bloodless Americanized adaptation of the play, as is his rant against majority rule; these omissions have the effect of making Miller's Dr. Stockmann into a wooden statue of righteousness--a pillar of society, if you will. Ibsen's doctor is a more problematic figure, and thus a more interesting one: ecologically, he's perfectly right, of course, but in his anger at the stupidity of those around him, he can sound like an Ayn Rand hero.
Part of the joke in Ibsen's version, likely to be lost on contemporary audiences, is that the printer Aslaksen also appeared in The League of Youth (which is not much performed these days). In the earlier play, he is a tippler; in An Enemy of the People, he returns as the local secretary of the Temperance Society. He is not a teetotaller, though:
Dr. Stockmann. Now, you will take a small glass of sherry, eh?
Aslaksen. No, thank you; I never drink alcohol of that kind.
Dr. Stockmann. Well, what do you say to a glass of beer, then?
Aslaksen. Nor that either, thank you, Doctor. I never drink
anything as early as this.
[From Act II; emphasis added. A good actor could have a lot of fun using these lines to make Aslaksen's back story clear to an audience unfamiliar with The League of Youth.]
Rather, he is an advocate of moderation in all things--moderation in drinking, moderation in morality, and especially moderation in being chased around the room by an umbrella-wielding doctor. Aslaksen's last line (in the next node), as he slinks out of the doctor's house, is translated here as "If only I knew the way about here--"; in the original, it's an echo of a catchphrase that he keeps repeating in The League of Youth (generally rendered as something like "local conditions").