As is often the case with these "I'm so smart and other people aren't" posts, the author makes what I bet is an unintended mistake. I assume they want each option to have only one solution. The last example ("It is poor form to ____ you temper in a discussion group"), either option (lose or loose) works. The verb form of 'loose' means 'to set free', and temper has come to mean an agitated state of mind. So you can say, "It is poor form to lose (be deprived of) your temper (calm state of mind) in a discussion group."
But you can also say, "It is poor form to loose (let free from restraint) your temper (agitated state of mind) in a discussion group."
One would loose one's temper \on\ a discussion group, not \in\ it. I enjoy the perspectives of the ESL folks on HN, though, so I don't want to see any filtering by grammar nitpicking.
I like the ESL comment: that's cute. But to your broader point I ask, "Why?" If I can comment in an online discussion group or I can post on an online discussion group, why is the relation of my temper any different than the relation of my post?
The OED is useful here: it literally defines in as equal to on in the second definition of the prepositional form of 'in'. There's an extended history of the relation between 'in' and 'on', which includes the Latinate source of the Saxon term, its evolution in Old and Middle English, and its use today. Suffice it to say, the distinction is not a trivial one, and 'in' and 'on' are often interchangeable.
Actually, I realize I squeezed in let without noticing. Try this...
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"on" sounds much more natural to me, and I think that's enough for me. Idiom counts in a language, too. In and on might seem technically interchangeable, but (sometimes) if it sounds wrong, it's wrong.
You can say, "I lose my temper." So like you can say "It is poor form to sleep in a meeting.", you can also say, "It is poor form to lose your temper in a meeting."
As someone else commented, you definitely can say, "I let loose my temper." So, "It is poor form to let loose your temper in a meeting." is fine.
But, can you say, "I loose my temper."? I think you can, but it is very very unnatural.
My thought process was that the online discussion group is the target or the victim, not the venue, of the loosing. In which case "on", or "at" for some other direct objects (like "arrows") would be the appropriate preposition. As in, I loose my temper (the hounds) on the unfortunate souls of Hacker News.
I agree with jmilloy, actually; regardless of whether or not that usage is correct, given that poems frequently flout grammar "rules" I don't think using a poem as evidence of a particular rule is a strong argument.
OP said "I don't think anyone would ever use loose in that manner without preceding it with 'let'". I provided a counterexample, so the OP's statement is refuted. Now, granted anyone could write a nonsense sentence to refute any rule of grammar. But this is a very important poem by a prominent poet.
I think that my comment came across as an attack. Rather, I just find the ways in which poems can interact with and affect existing, seemingly fixed aspects of language are beautiful and interesting! And in particular, it means that poetry has a unique place in discussions about both proper grammar and common usage.
You make a good point that you were furthering discussion about common usage and not necessarily grammar.
It's correct without "let", but a little archaic. You're unlikely to see that sort of usage outside slightly pretentious plays, but it's correct nonetheless.
But you can also say, "It is poor form to loose (let free from restraint) your temper (agitated state of mind) in a discussion group."