So much to unpack here; the implications that Devil Sword Sparda perhaps has a mind of its own, a piece of Sparda and it was no accident the sword and Dante fell so close to each other after facing Urizen: Sparda's soul was protecting his son by concealing his presence from predators for months. Dante was slumbering in Sparda's shadow.
Second: V may not be 100% Vergil but shares many of his traits including the belief that Dante was the chosen favourite...Vergil believed their mother, Eva died protecting Dante while he was left behind. And now he witnessed their father, Sparda protecting Dante. To V/Vergil, Dante was the favorite "chosen" child. It wasn't true of course but the circumstances fed that belief.