This is technically correct, but no context is devoid of political overtones and there's very reasonable arguments for decolonising the terminology.

"British Isles" is the widely accepted term internationally in large part due to the historical dominance of the British Empire, coupled with the ongoing influence of the British state internationally (particularly in the anglosphere). It is however not a generally preferred term within Ireland, which is worth noting alongside any technical facts about geography.

You're correct, and I'm British, but it's not surprising to me that an Irishman would object to it.

Besides, to us 'English Channel' is a geographic term; in France it's La Manche ('the sleeve'). (Having said that we do say 'Irish Sea'.)

Quite correct. Just like “GB” (“Great Britain” or “Grand Bretagne” in the original French) means “large Brittany”.