Extreme pet peeve

I do this to make it clear exactly what I'm responding to, not to twist or distort the original comment, particularly if the post contains a number of statements and/or if there have lots of other posts before I respond.

I don't mind if other people respond to my posts in that way, as long as they aren't in fact distorting what I've written - that does annoy me

I understand completely and agree with you OP. There is one person in particular who does this and does this quite often to "prove" their point and usually does it to attack any person who has a different opinion to theirs and then makes spelling mistakes in their own rants while pointing out the other person's faults. Enraging I agree but not worth bursting a blood vessel over.

I do this. I don't believe anyone should apologize for being thorough . . .

I suppose it is normal to be annoyed at being so thoroughly incorrect.

Seems like the best way to address all the points a post. What is the superior method of internet arguing you have to offer?

"My heart starts to beat...online...Is it normal that I find this enraging?" Nope.

we just like questioning your beliefs to see if you can back them up with facts

This has never happened to me on this site. If it did, it wouldn't upset me. I have bigger fish to fry.

I think Socrates' death could have been averted if he stayed away from folks like you.

All joking aside, it really doesn't bother me that much when people put things I say in quotations, and I even do it myself sometimes (complete with needling and snarky responses). I take great precautions to phrase everything as simply, but as precisely as possible. If misrepresentations are occurring even after you've attempted to remove all ambiguities from your speech and be direct, the person in question is either only hearing what they want to hear, or is purposefully arguing in bad faith and attempting to make you and whatever point you're arguing look bad (and is therefore not worth wasting time on). Internet debates aren't always the best way to engage people on a critical level anyway - the medium, especially when audiences and ranking systems of people's opinions are involved, tends to promote conformity, flash over substance, and general prickishness.

"Most of the time I cannot even continue to debate with said person if they begin to use this tactic."

They're making multiple points, how can I compete with this argument?

"It's like nails on a chalkboard, except it's ten chalkboards and a roomful of women with three-inch artificial nails."

Because all women are annoying and fake??

I'm joking, but it only annoys me when they purposely twist one thing you said into something else. Other than that, it's just a thorough way to argue.