Nero is not Vergil's son. Nero didn't recieve his demon powers till just before DMC4. If you pay attention to the story you would know that's true because EVERYONE is surprised about Nero's arm, these people he's been living his whole life with. Even Nero talks about his arm(the only demon part of him) it's in a tense that shows there was a time he didn't have it. Nero's a human that somehow ended up getting an arm that has "some connection" to Sparda. That's it.
There is no evidence Nero has anything to do with Vergil outside they both used Yamato which means jack nothing. It's just as plausable that Nero is the 3rd Son of Sparda. We at least KNOW Sparda was actually there in Fortuna & since he is AFK, there is no reason why he couldn't have fathered Nero.
*There is no proof showing that Nero is a full human before getting the demonic arm.
*It's not that Nero used Yamato... it's that him awakening his Devil Trigger reforged Yamato telekinetically. And then why would Nero utter "I need more power"?
*You just said that Nero is a human... but now you are saying he could also be Sparda's son which would make him half demon just like Dante/Vergil. So you are contradicting yourself.
*How do you counter this statement of Dante to Nero when referring to Yamato:
"I can't have something of that kinda power floating around now, can I? It's got to stay in the family."
Why can't Dante keep Yamato yet Nero can? Dante let's Nero have it despite making that statement. It's because he knows that Nero is Vergil's son and Yamato more rightfully belongs to Nero, not himself.
*In the DMC4 novel it's already been confirmed that Nero is Vergil's son. A guy at Capcom has also stated it before. People on the inside have confirmed it as well. As far as Capcom is concerned this is the canon.
*Sparda isn't AFK he is dead. He is more dead than Vergil.
I guess DMC4SE has to explicitly state in game that Nero is Vergil's son for people to believe it.