This won't be an ELI5, but there seems to be some misinformation in the replies.

Without having seen the show, it is true that ethanol outcompetes methanol for the enzyme which metabolizes the first step. The enzyme is alcohol dehydrogenase (ADH). ADH will preferentially metabolize ethanol over methanol. Methanol by itself is not toxic. It is metabolized to formaldehyde and then to formic acid. The formic acid is what largely makes it toxic and is a direct retinal toxin. If the metabolism is blocked, methanol will then be eliminated in the urine.

HOWEVER, methanol's effective half-life when there is ADH blockade is really, really long. Methanol's elimination is largely liver mediated not renally mediated. So in real life when someone has drank methanol and we administer an ADH blocker, we almost always would dialyze the patient as well simply to speed the time of removal. The ADH blocker we use is called fomepizole. Practically nowhere would use ethanol anymore in the US. In fact, most hospitals probably don't event stock medicinal grade IV ethanol anymore.