I’m a head cannon machine lately. 
Scuse me while i slap down my Inigo and Severa headcannons

In their child days, when they were being raised they lived pretty far from each other, yet Cordelia would go and visit Chrom from time to time and would bring Severa with her. Severa, as a child, was very fickle and pulled at Inigo’s hair, which caused him to cry.

So as they grew up they basically did not like each other. And it wasn’t until Severa and Inigo got to the future that they actually started to talk to each other.