I'm not Irish, but very light skinned. I've never been able to tan - I burn, then peel, then freckle, then back to pale.
Most people can tan, at least for a while. They don't understand that light skin doesn't mean you are a vampire and always hiding from the sun. They think everyone can tan, but you choose not to - which isn't always the case.
I would take this comment as a misunderstanding, but I agree that if it bothers you a lot it might be just the tip of the iceberg of misunderstanding.