Sorry, but the author is a complete idiot and transphobe.
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Her "straw-man" argument technique isn't very effective, nor is it logical.
Aside from that, she has a very warped and overly-simplistic idea of what privilege means. No concept at all of gender. And well...there are many other examples in that rant of someone who doesn't have all their threads of thought stitched together cleanly.
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Replace the word "trans" with "black" in the article. See if that wouldn't offend most people by trying to deny historical white privilege in this country. Her argument about -cis privilege is about as convincing.
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"like race-based power, gender-based power operates in one direction only: male-oppresses-female."
This pretty much sums up her skewed viewpoint. Apparently there are no women in this country that have any power over men. No man-haters that abuse that power. No blacks who have power in their communities, or who use that power inappropriately based upon racial preference. All minorities are pure angels and the only oppressors are white men? Wow...how archaic and simplistic of a view can you get? She's about 50 years behind the times (not that it was even that simple back then, but her viewpoint would have been more accurate long ago in the past), but she does appear to love being queen of her very own pity party.
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Someone who fails completely to see the difference between sex and gender will never understand the power dynamics involved in -cis vs -noncis. It's like trying to describe racism to someone who refuses to acknowledge the existence of skin color.
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meh...I could go a lot further, but that's the sort of idiot that really isn't worth another word's effort.