It is an idiosyncrasy of the language, much like in English we say, "The Ukraine" or "The Netherlands" when neither needs that distinction. It is why so many people mistakenly call the city in Portugal, "Oporto" when it is linguistically O Porto, or simply, in English... The Porto. :D
JK, of course (on that very last bit, it is really just Porto in English; and there is a reason for it as it used to signify "the port"). :)
BTW, the articles in front of the possessives are more widely used in Portugal (and the other Portuguese speaking countries and territories which all follow the Lisboa lingual conventions) than Brazil.
strange - I know that when you use teus or seus it implies to the possession but you cannot determine for sure if the possession is to one or the other, since teus behaves the way it does because of the object it describes (livros - plural-masculine this case). So - answering - "She reads your books" is valid as - "She reads her books" or "She reads their books". For some reason the app only accepts the first option... :(
Because "teu(s)/tua(s)" is only applicable to "your(s)" (Second Person "tu" which is the familiar).
"Seu(s)/sua(s)" is the one that is ambiguous (because while "você" refers to the Second Person it is actually a Third Person treatment just as much as "o senhor/a senhora"). So, "seu(s)/sua(s)" could be "his/her/your/theirs" and "its" (and probably one or two I left out :D).