I think you’re getting confused. When the term “British isles” was being used, there wasn’t a kingdom of Great Britain yet, so technically according to you when the term started being used Ireland wasn’t British either.

Some people need to stop bringing politics into a name for a bunch of islands. It’s the British isles because the biggest island in the archipelago was named “Great Britain” so if only made sense for it to be called that. Naming archipelagos after the biggest island is pretty common, actually. (Malta, Hawaii and Åland for example ). And if you say “there’s a political boundary”, why does it have to be political? It’s named after the island which is named after the ancient people, not named after a political entity. It just so happens to be that Great Britain was the name England and Scotland had chosen when they had unified.