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Why are the conditions for the elimination of halogenated hydrocarbons in the book methoxy anion and alcohol?
See Basic Organic Chemistry Higher Education Press.

The reaction mechanism of elimination reaction: E 1 and E2 principle,

E 1 mechanism: for example, in the absence of alkali, the reaction of tert-bromobutane is divided into two steps, first forming carbocation, and then adding or eliminating carbocation.

E2 mechanism: Secondary bromoalkane and tertiary bromoalkane react in weak polar solvent (ethanol) under the action of alkali. With the increase of alkali concentration, the proportion of eliminated products increases, which is a bimolecular process and the reaction kinetics is second-order reaction.

What you said belongs to the E2 mechanism.