The British Isles is also a somewhat controversial term with colonial implications, and it's not used by the government of Ireland[1]. "Britain and Ireland" would be a safer bet, as the map doesn't include any other islands.
Diving into Wikipedia, apparently variations of the name "Britain" have been in use since 30BC, and referred to the big island, with the smaller islands grouped with it, e.g. British Isles.
The Irish may not like it, but they're fighting against two millenia of history.
Sure, but more recent history should have a higher weight. It is reasonable that our names for things reflect recent history and current affairs more than ancient history.
Two thousand years ago Britain and Ireland were ethnically and linguistically pretty similar (I believe). Since then they have diverged in many ways - most significantly during the Reformation period when people in Britain largely left Catholicism, but people in Ireland remained Catholic. Changes like this and the legacy of colonialism this have ultimately resulted in Ireland having distinctly non-British identity. It is reasonable that our naming for things reflect this current state of affairs.
As always, it useful to consider other examples to clarify the point. For example, by the same argument, should we deprecate the phrase "Latin America"? After all, Latin Europeans only arrived in the Americas 500 years ago and the continent has had people for 10 thousand years before that. Are people who include a European adjective in the name of this cultural area "fighting against ten millenia of history"?
And it's use in English only comes from the mid 16th and 17th centuries, right around the time that much of Ireland was being colonized by the British.
Frankly, I find the term offensive, and think it should be discouraged in much the same way people have shifted away from "the Ukraine" to simply Ukraine.
There’s not a 100% great term for the collective unit of land. Generally people go with “UK & Ireland” if they’re trying to be sensitive.