Why doesn't this reaction use an E2 mechanism?

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The discussion centers on the reaction of tert-butyl bromide with methoxide (MeOK) in methanol (MeOH). The key point is the expectation that MeOK dissociates to form MeO-, a strong base capable of initiating an E2 elimination reaction by abstracting a proton from tert-butyl bromide. The tert-butyl bromide's tertiary carbon creates significant steric hindrance, making SN2 reactions unlikely. Consequently, the focus shifts to elimination mechanisms, specifically E2, as the most probable pathway. Although SN1 and E1 reactions could theoretically occur, their contributions are deemed negligible due to the strong nucleophilic nature of MeO- and the steric constraints of the substrate. Overall, E2 is favored in this scenario due to the combination of the substrate's structure and the reactivity of the base.
gauss44
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tert-butyl bromide + MeOK in MeOH ----->

I would think that MeOK would dissociate in solution making it MeO- which would be strong enough to yank a proton off tert-butyl bromide and initiate an E2 reaction. Where am I going wrong?

PS - I am a tutor who hasn't done organic chemistry for a while, so please leave this here AND do NOT send me to the ¨Homework¨ section. This is NOT homework.
 
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The central carbon atom in tBut-Br is tertiary, which gives rise to high steric hinderance, which means that we can exclude Sn2, leaving E1, E2 or Sn1. Continuing, if we consider the other reactant Me-OK, it is negatively charged and thus a strong nucleophile/base. However, since it is strong Sn1 or E1 are unlikely to happen, leaving us only E2 to happen. Don't forget though that Sn1, E1 and Sn2 will happen, but it is to a such small extend that it can be approximately unconsidered.
 
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