Counter-arguments

A. Latin and ancient Greek are dead languages

In fact, Latin or ancient Greek are nobody's mother tongue.

But a dead language may be more suited than a modern one to learn the basics of grammar and of language as such,

... and authors such as Aristotle, Plato, Cicero, Horace, or Seneca are not less influential than Dante, Shakespeare, Goethe and many others; and certainly the former strongly influenced the latter.

B. Learning Latin and Greek is pointless, stupid cramming

Admittedly, a lot of grammar and vocabulary has to be learnt, and this can easily drive you to your frustration threshold,

but by continually and systematically learning things you develop and get used to learning strategies, get self-organized, deal with frustration, in short, you learn how to learn on your own, ... and not just ancient languages.

C. Latin and Greek are difficult

It is true: thesaurus and grammar are remarkably rich, complex, and demanding, ... but that applies to many modern languages as well.

Regarding spelling and pronunciation, the ancient languages are no doubt easier than, say, English or French.

D. Latin or ancient Greek are useless

In fact, Latin or ancient Greek don't play a direct role in industrial or agricultural production processes.
So everybody planning her or his future career in such a field may be better advised to attend a more specialised secondary education lacking the ancient languages.

However, learning Latin forms important competences such as
accuracy, the ability to combine and comprehend, problem-solving strategies, and thinking, ... all of which are tools that are extremely useful for everybody in a large number of practical fields and situations.