Nagini is a horcrux and can't be killed with a wand! The only reason the Sword of Gryffindor works is because it absorbed the traits of basilisk venom. Basilisk venom is one of the only things that can destroy a horcrux!
And also--his greatest fear was SNAPE. He was afraid not of something that he might one day run across, but of someone who actually made his life hell. He was afraid being bullied and belittled. And everyone laughs about that, but it's heartbreaking.
I love Snape and believe that he hated Neville because in his eyes, it should have been him & his parents targeted by the Dark Lord. Good job for Neville for being the amazing professor that kids can turn to ♥