Also he had many ladies hitting on him (mia, marcia, lete, elincia, the merchant...) and he had no interest.
Since I've already answered the part about Soren, I'll move on to this.
Aimee the merchant is like that annoying girl in high school who keeps begging the school quarterback to go out with her, despite him telling her that he's not interested. It's not that he's gay, it's that she's so **** annoying with her persistance that it turns him off to her.
Mia wants a rival to train with and become stronger, not a lover.
Marcia doesn't hit on Ike.
Lethe? He actually responds fairly favorably to her, and in their PoR A-support he considers moving to Gallia with her later on to become stronger (granted, he apparently decides not to, but anyone who's played Radiant Dawn knows that by then he'd gotten to the point where Tellius didn't have anything left to teach him and he decides to explore the rest of the world).
Elincia is only a client to Ike who respects him highly. She is actually in love with Geoffrey.