George Michael (the dorky kid on the show, not the singer-songwriter) believes doing well in math is necessary for success. He also thinks failing math is sufficient to destroy his chances at success. (Learn about necessary and sufficient on Wikipedia and in this week's blog post on necessary and sufficient conditions.)
You can watch this clip in the video below, in this link, or you can just read the quote. You'll probably enjoy it even more if you watch the whole 20-minute episode, but watching it isn't necessary to understand the LSAT-related part.
The quote starts at 5:37 in the video. George Michael (a classic burnout case) is doing his homework when his dad walks in...
George Michael (Michael Cera): [Arguing with his math book] Dumb, dumb George Michael, dumb...
Michael Bluth (Jason Bateman): Hey, calm down there, you two; it's just a math problem.
George Michael: Yeah, but if I fail math then there goes my chances to get a good job and have a happy life full of hard work, like you always say, right Dad?
So what's wrong with George Michael's statement?
Necessary and sufficient
George Michael assumes failing math is sufficient to end his chances of getting "a good job and...happy life full of hard work." There might be ways for him to get that "good job and happy life full of hard work" even if he fails math.
Another way to say this is: George Michael believes not failing math is necessary to get those things. We only need one example of someone who got those things after failing math to disprove the principle underlying his argument.
Appeal to authority
George Michael makes his argument simply by appealing to his father's authority. Citing an authority doesn't count as sufficient evidence for any argument.
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Believe it or not, even after searching through a comprehensive list of Arrested Development quotes, I was unable to find any examples of actual logical fallacies made by "Gob" (played by Will Arnett).
Arrested Development fans, please post examples of logical fallacies from any character in the comments.

