Languages have different ages. Now obviously you can’t ever draw a clean, exact line between when one language becomes another, but there are also clearly distinct languages and those distinctions can be given upper and lower bounds in terms of dates.
Latin is clearly distinct from English, even though both languages share a common ancestor and English itself was heavily influenced by Latin, both directly and indirectly. Yet it is still useful to make the distinction between them as separate languages and what we call Latin is clearly older than what we call English.
I don’t think it’s at all useful to say Latin and English are the really the same age, even if it’s technically true per your definition.
It's a bit like saying all species are the same age because we all share a common ancestor and there's no exact date when you can say one species became another.
Latin is clearly distinct from English, even though both languages share a common ancestor and English itself was heavily influenced by Latin, both directly and indirectly. Yet it is still useful to make the distinction between them as separate languages and what we call Latin is clearly older than what we call English.
I don’t think it’s at all useful to say Latin and English are the really the same age, even if it’s technically true per your definition.
It's a bit like saying all species are the same age because we all share a common ancestor and there's no exact date when you can say one species became another.