Your GM has just taken away your narrative authority over your own character by making them do something you would never do. This makes you feel, Hungry. Sleepy. Indignant.
You're playing an RPG with it's writer but he wants to demonstrate the setting rather than let you play. This makes you, Superflous. Fastidious. Giddy.
the problem with that is that you can still break it fairly easily - I recall one approach where the scammers/spammers used a strip poker type app where "players" had to solve captcha to see nude photos of a woman, another one would be Amazon's mechanical turk I guess.
And Rob is right - while in the sample case, it's fairly obvious what the right answer is, it's conceivable that other issues are more ambiguous. And then there's the question of whether you really want to turn captcha's into a political instrument.
Still I suppose it's better than normal captchas - I regularly come across captchas I can absolutely not read (I am colorblind).