Virgil in Pokémon is supposed to have every version of Eevee's evolution so why doesn't he have a Sylveon?
That's because Virgil and his team of Eeveelutions appeared in "Team Eevee and the Pokémon Rescue Squad!"(November 15, 2012) which was the second episode in the Black & White series.
The Black & White Series was part of Generation 5, Sylveon was introduced in X&Y which is Generation 6 and debuted on October 12 2013, nearly a year later.
So the reason is because the Pokémon did not exist yet. Same reason why the The Battling Eevee Brothers (April 16, 1998) only had Vaporeon, Flareon, Jolteon and Eevee seeing the others did not exist yet.