According to embryology, why do fish and birds have a common ancestor?

sheep is a herbivore animal whereas grasshopper belongs to the class chordates but both of them feed on greens.  

if grasshopper and sheep feeding on a pasture land, i do not think both of them will have any impact on each other. however, the number of the species can make difference. since sheep feed on greens, there is a possibility there left no pasture land for the grasshoppers or they may get extinct.