That wasn't the only reason. Just read the questlines in the blood elf starting area. At the beginning, the blood elfs are rather neutral, however, due to some Alliance spys in blood elf territory and the fact that the Horde were the ones who actually helped them (Forsaken) taking back their territroy and fighting back the scoruge, it was a rather easy decision. Furthermore, night elves and blood elves still don't have much love for another, especially since the highborne have rejoined the night elves and are allowed to practice magic, something the blood elves were ejected for. To the blood elves, the night elves are hypocrites. The cleaning of Dalaran just strenghtened the distrust and hate of the blood elves against the Alliance.