Guts left the Hawks because of Caska. Falling in love with Caska was too much for his attachment to his allianation that winter. He wanted to overcome his own allianation by himself and not because of Caska so he left.
Guts didn't leave the hawks because of Caska. He left because of Griffith. Because what Griffith said about a friend being his equal. Guts left to become Griffith's equal, not because he was falling for Caska.