Nilay's answer, as well as the comments, do a great job of explaining why methanol is toxic (and ethanol is comparatively less toxic). I'll take a different approach here: I'll explain why ethanol is the major component of alcoholic drinks. To start off, ethanol is not the only alcohol in alcoholic drinks1. Other alcohols such as Glycerol, Tryptophol, Tert-butyl alcohol, Tert-amyl alcohol, Phenethyl alcohol, Propanol, etc are also present, though in smaller amounts.
The main requirement of an alcohol in a drink is to produce the feeling of intoxication: The most common Alcohols satisfying this are Ethanol and Propanol (which is 2-4 times more potent than ethanol). While these alcohols give you a tour of the skies, Toxic alcohols take you straight to heaven, and are a strict no-no. Other requirements include solubility: due to a larger hydrocarbon portion, propanol is less soluble than ethanol in water. This is not a problem for beer, but can be a problem for spirits (which may have up to 40% ethanol).
The simplest reason for the usage of ethanol over propanol would be because nature has willed it so. Zymase is the enzyme that fermentation bacteria use to convert glucose to ethanol, and there is no common analogue that creates propanol from glucose. Ethanol has been used for beverages since the time some farmer left some foodgrains in water for a long time, and later got a good feeling on drinking that water. There is no intertia to change, ergo we continue to use the same process for creating drinks even today.
- IARC Working Group on the Evaluation of Carcinogenic Risks to Humans. Alcohol Drinking. Lyon (FR): International Agency for Research on Cancer; 1988. (IARC Monographs on the Evaluation of Carcinogenic Risks to Humans, No. 44.) 3, Chemical Composition of Alcoholic Beverages, Additives and Contaminants. Available from: https://www.ncbi.nlm.nih.gov/books/NBK531662/