It's not about intellectual property, it's an "it's the thought that counts" type of thing that is hard to explain to outsiders. In several cultures, singing someone a song is a very personal act of gift giving in which the singer creates beautiful sound just for the listener(s) - it is as much an expression of the relationship between them as it is about music or poetry. That latter bit is often lost in developed countries that have established musical industries instead of a vast array of amateur bards.

Just like it is considered inappropriate to give away something that was a gift to you in many cultures, in some it is considered bad form to appropriate someone's expression of emotion unless you were invited to by the singer.