Because of certain humorous cultural stereotypes associated with the ancient Greeks and Very Young Men, it might be best that I dispel any inchoate notions forming in your head.
The Very Young Man muses on all the wonderful opportunities such a Time Machine could afford him. He could learn Classical Greek from Classic Greeks!
However, if he did that, The Time Traveller replies, his teachers would plough him for the Little-go.
In the UK, plough was once used as slang for "fail":
plough (TFD): 12. (Education) (intr) Brit to fail an examination
And the Little-go was an informal term for "Responsions"¹, one of the three tests all students of the University of Oxford once needed to pass to earn a degree. Per Wikipedia:
Responsions was the first of the three examinations once required for an academic degree at the University of Oxford.
It was nicknamed the Little Go and was generally taken by students prior to or shortly after matriculation, the idea being that without standardised qualifications from school examinations, the University had to verify for itself the quality of the students that colleges were accepting. The examination consisted of comparatively simple questions on Latin, Ancient Greek, and mathematics. It was abolished in 1960.
Of course, knowledge of Ancient Greek being a staple of a classic education at the time, the Little-go would test The Very Young Man's knowledge of it.
And, just as obviously, if he had learned Ancient Greek from actual Ancient Greeks, directly, he would have failed that test.
Because, of course, modern teachers don't know how actual Ancient Greek was spoken; they only know the reconstructed and speculative version the "German scholars have improved upon".
And if you don't believe me, maybe you'll believe The Schmoop:
You could study Ancient Greek in Ancient Greece so you could pass your tests! But since you'd be the only modern person who really knew Ancient Greek, your teachers would fail you. (That's what "plough you for the Little-go" means – it's not as dirty as it sounds.)
Now get your mind out of the gutter.
¹ Speculation: Little-go because the test was a go (attempt) at your degree: the first, easiest, littlest of the three.