Thank you both for your comments. In the meantime, a Greek friend sent me a definition of the word 'hybrid' from a Greek dictionary. It seems that 'υβρίδιο' comes from the Latin hybrida/hibrida/ibrida, which in turn comes from the Greek hubris/hybris - 'ὕβρις'. 'Hybris' originally meant:
1. to go beyond the human nature and act superciliously;
2. impudence as a result of extreme passion or a sense of being excessively powerful
So, I understand that the word (the signifier, the sounds) circulated back and forth, with a changed spelling and apparently another meaning, more connected with biology rather than with morality. To continue this speculation, I wonder why Latin language lost this reference to having the power of going beyond the human nature, why this power was considered supercilious.
One reason could be that in Antiquity they did not have dictionaries. But perhaps there are other reasons too.
And then no wonder that English somehow lost this Greek origin. Even though definitions include not only meanings related to biology and order, but also to technology and to morality, the latter are not reflected by the Latin root.
The Greek source is here:
http://www.greek-language.gr/greekLang/index.html