The how is not yet worked out. The why is 'cause Nero's given a lot more Sparda traits than either Dante or Vergil--and a huge deal is made out of Nero having fallen for a human, just like Sparda. Nero still uses Yamato, though, and has a lot of Vergil lines. And apparently hears a voice in his head that says, "I need more power." So I don't know.

He's probably right. A lot of the official art from the first game has her hanging all over him, and apparently the recap calls Trish "Dante's love," so.