From what I saw in mlp, some look of the villains of the season have a Freudian Excuse, something that happened in their lives that made them that way:

Nightmare Moon- feels overshadowed
Discord-Never had a friend
Sombra-comics said he was an outcast among the crystal ponies
Tirek- Jealous of his good brother
Starlight-traumatized over losing her friend due to his cutie mark
Chrysalis-obviously, she doesn't want to share love because she's scared of transforming.
Stygian-felt betrayed by the pillars

But was is Neighsay's excuse? Something made him think non-ponies are bad. Here are my theories:

Grew up in a family of haughty unicorns, descended from Platinum.

Had his cutie mark scratched by a nonpony since we haven't seen his mark

Lost a friend because a nonpony attacked that friend. Hint: she was in a movie

Maybe.

Speciesism, not racism.
One doesn't need a direct reason to be racist and/or speciesist , just a sense of self preservation and/or day to day bad experiences.

And Equestria experienced lots of problems with non-ponies that more than warrant being called bad experiences and even more so justify the need for self preservation, invasions by changelins and the Storm Kingdom, almost being declared war by Yaks and Dragons for stupid reasons. not to mention the poor state of the griffons, poor state that could, coupled with their greedy nature potentially have resulted in (unmentionned in the show but a possibility) thief and murder across their nation (remember the griffon that would have left Rainbow to die because she didn't have money?).

And that is just on the fly and without mentionning the likes of Tirek and Discord.

6539122
Oh I like the idea of having his cutiemark maimed by a nonpony.

6544092
Not to mention that he raised legitimate complaints about how the school was run.

Catrina37: Lost a friend because a nonpony attacked that friend. Hint: she was in a movie
Me: Tempest Shadow?! Wait so that means Neighsay And Tempest Could be childhood friends. No wonder why I made a romance story about them called Space Between

6539122
He's a byproduct of Celestia's rule which says a lot more about her than it does him, not to mention the Canterlot Wedding Invasion by the Changelings and the Storm King's invasion at the Festival did not make the other species look good in Neighsay's eyes.

L

ost a friend because a nonpony attacked that friend. Hint: she was in a movie

They eventually met each other again in The Ending of the End-Part 2

AND THEY FELL IN LOVE!!! 😍 jk...