All Virgil did was react to what Dante did. Same goes for the first fight. Dante was the first to point his guns. Dante's fear gets the better of him. Good intentions and all.I mean, what was Dante supposed to do? Ask Vergil if they could hold hands and sing kumbaya as they walk out of the tower together? No, he's there to stop Vergil from opening the gates to Hell and dooming humanity. He knows that Vergil isn't going to stop without Dante resorting to force and so of course he comes with his sword at the ready. :/
Why provoke a fight when words are causing Virgil to pause and think? Answer: Because Dante acts in haste. The fight weakened both him and Virgil and gave Arkham the upper hand.
What virgil does is use your own fear against you. The cutscene where Dante rushes in blind and gets knocked onto the floor in 5 is the perfect example here. When is Dante going to learn the folly of rushing in blind?
Simply put, Dante is conflicted with himself. Let's take the cutscene where Urizen eats the apple for example. When Dante is trying to talk Urizen out of it his face is clearly struggling. He's not convicted enough. He's been refusing to listen to conversations in the past (angi and rudra in 3 alone is just one example). He wants to get through to Virgil but he can't quite figure out how. He pauses. Hesitates. He's not as capable as he might pretend to be. And Dante knows it.
Compare that to Nero, who doesn't hesitate for a nano second. I imagine he's been called out a lot more because of Credo if nothing else. Perhaps Credo pushed Nero to do better when he struggled. Regardless, Nero doesn't wait for a moment. He isn't pausing. He's got that conviction and he gets things done. This is the difference between Dante and Nero. If you don't believe in yourself then why would others?
On that note it would be interesting to know more about Credo. He's that "no nonsense" type. He's dead now though. But it's still interesting to think about what influence he might have had on Nero. Credo seems to have been something of a mentor for Nero. If so then this also helps explain why Nero decided to make everything his responsibility in the end.