It is the 'pure-ness' of the language that makes Greek and German better for philosophy than, e.g., English.
As you read Heidegger in German or translated in a language close enough to keep all or most of the word-play intact (e.g., Dutch), you'll see the way he builds up his insights. This word comes from this and that, in this and that way it means such and such, but in this and that sentence it means something else, so how is that possible; what is the common root, what is the basic meaning that underlies both differing specific meanings; how is the derivation or development of this to be explained; etc. This technique doesn't make for his strongest arguments; but it provides him the basic elements with which he builds his thinking. If you accept his thinking in the larger picture, you can't get around his way of using etymolog; you'll have to become creative yourself in playing this game.
English is a mixed-up language. The core feeling of it is Germanic, but it has an insane amount of loan-words from Latin. If you take any German or Dutch stem-word from which a long list of derived words can be made, and you translate that into English, you'll see that only the one stem-word in English is still of Germanic origin; the rest are all very different loanwords. Result: the underlying basic meaning cannot be traced easily. Result of which is English words will function like 'stickers': this means that, because we said so, just learn it by heart. German and Dutch words mean something because the words themselves say so. Basically, as an English speaker, you'll need to speak both Latin and German to understand your own language.
Example: here is a list of Dutch words derived from from 'spreken' (to speak). All derivations still show traces of 'spreken', 'spraak', 'gesprek'. In English only 'to speak' remains; the rest are Latin words, and not even from the same Latin word:
Spreken - speak
Aanspreken - address/ appeal
Afspreken - agree/ make an appointment
Bespreken - discuss
Gesprek- talk, conversation
(...) Inspreken - record/ leave a message/ encourage
Tegenspreken - contradict
Uitspreken - pronounce
Verspreken - make slip of tongue
Vanzelfsprekend - evidently, obviously, naturally, taken for granted
Vrijspreken - absolve, acquit
As for Heidegger's aversion to Romans and Latin (which is a pretty pure language by itself), this lies somewhere else, mostly. Also, it has to do with the fact that when the Romans translated into Latin (same argument as with English) they romanized everything, also the meaning of words.
But the way in which Heidegger places the Romans in his history of being is another argument. He really reserves a special place for them, as one of the historical high-points/deep-points of nihilism, only to be surpassed by Nietzsche and the technological age (the make-ability of beings coming to the foreground of understanding the world, and a subsequent ending of philosophizing as development of new Original metaphysical basic positions). To argue with this, one must find another way of engaging with Roman culture (e.g., their art; Heidegger focuses more on their politics and their (lack of) philosophy), because, in Heidegger's own terms, you cannot get around this role they played without changing the development of his history of being both backward and forward.