To be fair, if you start your response with "Your post is completely inaccurate", you are almost guaranteed to get a negative response. Like you said, the natural human reaction is to defend oneself when "attacked", even in a harmless constructive-criticism way.
I try to use the compliment sandwich - say something nice at the start and end, put the critique in the middle. Some people just want to force you to agree with them, no matter what you say they respond with a passionate defense of their ideas - perhaps not logical, but passionate - in these cases, I try to just step out of the conversation.
It's easier said than done to accept criticism well - I know I have a lot more work to do.
You're absolutely right. Coming off so bluntly probably didn't work well in my favor. Being more tactful and going with the compliment sandwich definitely would have helped my case. Thanks for the input!