The problem with arguing on the Internet is somewhat analogous to if a skilled swordsman wandered the streets offering a foil to random strangers to fence with them. The average person on the Internet is about as skilled at logical argumentation and rhetoric as he is at swordplay, having never touched a sword, but having watched a few Hollywood pirate movies.
But that's only the tip of the iceberg.
Imagine instead if the master swordsman handed a foil to a random stranger on the street and started fencing, but every time he got a hit, his foe said "no you didn't, that's not how the game works!" and insisted he was actually winning. Every time he did some kind of ridiculous Hollywood cinematic thing, he'd consider that he scored a point, but since the master swordsman wasn't doing those things, neither his foe nor the bystanders would accord him any points.
In the end, of course, the master swordsman would have had dozens of chances to maim, kill, or subdue his foe, and blocked every blow that came anywhere near being able to injure him. But no one else would realize that he won. They just thought he was dry, and kind of boring.
You can only win so many arguments against people who don't even realize what an argument is before it's not even amusing for its own sake.
(Months after I made this post, the following strip showed up on Cectic:)