Competitive inhibition.

Both methanol and ethanol compete for access the limited amount of enzyme alcohol dehydrogenase.

Methanol is converted to a toxic compound formic acid or formate. That's nasty stuff and your body can't really clear it. It needs to effectively kill the affected tissue and remove that, which takes days to weeks.

Ethanol is slightly better at binding to the enzyme compared to methanol. So if you have 95% ethanol and 5% methanol, practically close to zero methanol is being converted by the enzyme.

Silly analgoy: myself and a really attractive woman are both trying to buy a drink at a bar from the same bartender. A long enough queue of attractive women and I'm never getting a drink. So I give up and go home.

Methanol and ethanol are both removed by urine (and breathing + sweating). So long as the methanol is still circulating and not reacting with the enzyme, you simply urinate it out.