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personally i think byleth needs edelgard more than edelgard needs byleth
i like to imagine that byleth is moved by edelgards conviction and decisiveness. edelgard knows what she wants, she doesn't let other people control her. byleth is very used to passively letting things happen to her, just following orders of clients or her father or the church
i think byleth looks up to edelgard a great deal. emotionally, having byleth as an ally helps edelgard not to lose her humanity in the process of following her goals, but regardless of byleths presence in her life, she still does not waver
edelgard does tell byleth in their S support "i need you" but i dont think its actually true, even if she might feel that way because of how much she loves byleth. during the timeskip, she does despair at the lose of byleth, but that doesnt stop her
if she truly did lose byleth to death, of course shes only human, and would grieve, but in the long run i think it would eventually be something to drive her to fight even harder towards her goals just as her siblings do
