The toxic alcohols contribute to the high anion gap metabolic acidosis by becoming metabolised into organic acids which require buffering in the body fluids.
Pretty much every alcohol that is not ethanol is thought of as a "toxic" alcohol. And lets face it, ethanol is not that safe either. However, in contrast to the others, ethanol gets metabolised into acetate, which - though still an organic acid - can be metabolised rapidly, and thus be removed from the circulation. The other toxic alcohols get metabolised into molecules which are much more difficult to handle.
Let us observe the metabolism of methanol.
Note the transitional step into formaldehyde. This substance is far from benign. The formate at the end of the metabolic pathway is even worse,, causing inhibition of the cytochrome enzymes of the electron transport chain. This results in retinal damage, among other things.
This sort of accumulation of something deadly in the body fluids is a feature of all the alcohols, because they all go through the same metabolic steps. Observe:
The end products are organic acids which are difficult, slow or impossible to metabolise. The presence of these acids is the major vehicle for toxicity. Some of the generated acids make only a minimal contribution to the acidosis, and do most of their damage by some peripheral route (eg. oxalic acid, which crystallises in the renal tubules, causing renal failure)
As can be plainly seen, alcohol dehydrogenase is the common pathway for all of these toxins. It is therefore the most intersting drug target. With alcohol dehydrogenase blocked, the toxic alcohols on their own are rather benign.
Because of their good water solubility and limited tubular resorption, their renal clearance will usually be quite rapid.
So; there are inhibitors of alcohol dehydrogenase and aldehyde dehydrogenase. Meditating on this topic, one could find oneself inclined to ask the silly question: does consuming such an inhibitor together with ethanol result in a prolonged state of intoxication?
Why, yes, it does.
So why do we even have alcohol dehydrogenase?
Well. The whole alcohol/aldehyde dehydrogenase family of enzymes is ancient, and originates probably from the glutathione-dependent formaldehyde dehydrogenase. The most primitive organisms which contain the enzyme are actually yeasts - but for them, the enzyme works backwards, creating ethanol out of sugar. In this fashion, the crafty yeast fashions for itself an environment of such high ethanol concentration, that it excludes all other organisms. It seems all vertebrates possess these enzymes. A Baltic cod is surprisingly capable of metabolising at least as much booze as a teenager, gram for gram.
Needless to say, in most vertebrates the evlutionary persistance of these enzymes this is not the consequence of constant recreational immersion in alcohol, nor a constant competition with the cunning of yeasts. Instead, alcohol is frequently found in the animal kingdom as a metabolic end-product of anaerobic metabolism.
As far as accumulating metabolic byproducts go, alcohol is among the least dangerous - compare it for example to lactate in humans (which, by accumulating, significantly impairs one's mood.) Many species which rely on prolonged periods of anaerobic activity have a pathway whereby pyruvate, rather than being turned into lactate, instead is metabolised into acetaldehyde and then into alcohol.
And what does alcohol dehydrogenase do when we are not drinking? Well. It quietly toils to metabolise all sorts of bacterially derived alcohols. All those yeasty half-rotten foods our ancestors would have been eating had about 4% alcohol in them. Additionally, exogenously available vitamin A (retinol) is a toxic alcohol, and alcohol dehydrogenase is thought to be the main defense against retinol hypervitaminosis.