1. Because Greek was the language of pioneers of STEM in antiquity.
2. Because Greek was the scientific language of the Roman Empire, and as such kept contributing to the naming of scientific concepts.
3. Because Latin (with the Greek layer of scientific vocabulary included) was the scientific language of the West from mediaeval times up until the 1800s.
4. Because even when Graeco-Latin stopped being the scientific language of the West, enough of the scientific vocabulary had already been contributed into Western languages by Graeco-Latin, that new terms kept drawing from that source—for consistency and associated prestige, well into the 20th century.
Nothing to do with Latin being dead (which, as a scientific language, it wasn’t), stable (Neo-Latin wasn’t), or concise (if you want concision, you go to Greek, which handles compounds a lot more flexibly than Latin). Nothing to do with Latin being secret: all intellectuals in Europe understood it, and it was the language of the church that persecuted Galileo, as well. (Yes, Latin kept the Unwashed Horde out of science. Contemporary English-based jargon does just as well.)