I think this is set "Before" Cirno's declaration of being "The Strongest". As in, Yuuka is setting Cirno up to be "The Strongest", and in doing so make Cirno into a Youkai like herself.
BrotherJohn said: Maybe Yuuka want to train Cirno so they can spend more time together?
something like that yes
Cirno?I thought they would be frustrated.However,They challenged me, and threw every last trump card they have at me.Hey... Cirno.This kid here, came back....Don't you, want to be even stronger?In the end, I won the battle.Fear, hostility, admirationThe eyes looking at Kazami Yuuka always held such emotions.What Kazami Yuuka always wanted was now, right before her eyes."Maybe, if it's this child..."Such thoughts passed through her head, and she muttered without thinking.Spoken even though she understood what it meant.
It was too bright for the lonely Youkai's dry heart.But Cirno stared at Kazami Yuuka with eyes holding none of those emotions.Yuuka, why do you "also" ask that?I thought she wouldn't come back.