@tanguatlay,
Well, I can't explain that to you, but it is a settled convention of the English language that the period immediately after midnight is known as morning. It's one of those usages which is so common that one doesn't even think about it. Perhaps it is because last night could mean today or yesterday. As an example, it is now Saturday here as I write this. So if I wrote "last night" it would not be clear if I meant Friday or Saturday. But if I wrote: "Very early this morning, loud voices outside woke me up."--it would be generally understood by English-speakers that I meant in the nighttime hours of Saturday, before dawn.