It isn't "illegal" but there are negative consequences to doing so.
The civil penalties for failure to file a tax return are a percentage of the tax not paid (5% per month up to a maximum amount, plus interest). There is a small penalty for not filing an information tax return (like a 1099) when you have to file one and don't owe money, but there is usually not such a nominal fine for a personal form 1040.
The statute of limitation on IRS efforts to audit a tax return or to impose additional tax for additional amounts owed doesn't begin to run until a tax return is filed.
Criminal penalties require an intent to deprive the government of money.
If he had more withheld than he owed, he probably isn't subject to any realistic significant civil or criminal consequences, but it is highly risky if he actually owed more than was withheld from his paychecks, and it deprives him of an ability to get refunds if too much was withheld (and possibly also stimulus check refunds) after three years.
The issue here is really that it is hard to see that the downsides of not filing a tax return are hard to match to the benefits of filing a tax return, which for a wage and salary earning teacher, are very slight (you could pay someone to do it for $100-$300).
Also, the lack of tax returns could hurt the teacher if the teacher ever has to apply for credit or get divorced or file for financial aid for the teacher's own kids to go to college.
Of course, if he had lots of unreported side income, upon which he has not paid taxes, then there are serious civil and criminal consequences.