Why does English language etymology seem to show so many words with Latin or Greek origin? Perhaps I just don't notice words of Germanic roots.
The answer is pretty interesting.
The overwhelming proportion of the words of the English language are, as you rightly point out, Latin or Greek. This is particularly true as you get into "bigger" words which describe concepts or ideas.
However, the most frequently used words in English have Anglo-Saxon origins. For example, we kept the Germanic/A-S forms of the verb 'to be'.
Essentially, when English speakers needed other words, they reached out to other languages, and Romance was the nearest thing. At the same time, they kept the core of their language intact.
Hi! As mentioned, English is a Germanic language at its core (and maybe a topic better discussed in /r/linguistics), but of course there are many words from Latin via Norman French, Latin directly, and Greek. There have been a few discussions about words of Latin origin specifically; check these out for previous responses:
Words of Latin origin in English.