I suspect the "great" Britain distinguishes it from the other Britain which is a nearby French province, ie "Grande Bretagne" vs "Bretagne". Ireland is still not British! The "British Isles" was a useful term for a dominant power while it lasted.
"Claudius Ptolemy referred to the larger island as great Britain (μεγάλη Βρεττανία megale Brettania) and to Ireland as little Britain (μικρὰ Βρεττανία mikra Brettania) in his work Almagest (147–148 AD)"
I feel that the reference to English and UK colonial and imperial legacy is more a recognition that the term has in the present day become controversial, and, to some, offensive for a number of reasons which include: a history of oppression and/dominance, both within the archipelago and beyond; a jingoistic element within the UK population that considers that to be a good thing; the conflation of the various meanings of _great_
Those things are distinct from where the name came from ≈2,000 years ago, but speak directly to why it might be offensive today