Freud thought that all humans were born pansexual, and that homosexuality or heterosexuality was a result of environmental influences during childhood. The normal process differed for men and women, but for men it was basically about overcoming the Oedipus complex, the idea that boys focus on their mother as a love object and then see their fathers as their rivals for her attention. Then, as the boy develops into a man, he replaces his mother as the object of his love, focusing instead on an adult woman. Girls, on the other hand, were supposed to be fixated on the "masculine" clitoris in childhood and then, as part of their heterosexual development, shift that focus to the vagina. In Freud's view, homosexuality is basically a form of arrested development the same way an oral fixation or being anal-retentive is -- for whatever reason, you didn't complete your development, and now you're homosexual as a result.

Freud's influences regarding homosexuality weren't people who thought about homosexuality as a mental illness. If you read the full letter that that quote is from, Freud actually tells the woman he's writing to to go and read the work of Havelock Ellis, who was a popular sexologist at the time. Ellis' theory about homosexuality was that it was a benign genetic variation, not a degenerate personality type. He believed that it was impossible for gay people to suppress their desires and that attempts to do so would make that desire "perverted", not the desire itself.

While some people disagreed with Ellis, the position that homosexuality was harmful was not universal among sexologists and psychologists. While some sexologists thought of it as perverse (for example, Richard Krafft-Ebing), others, like Karl Ulrichs, also thought of it as harmless. Before the Nazis, Germany was also probably the most progressive country in the West with regard to sexual studies. A lot of prominent scholars, like Magnus Hirschfeld, went even further than Freud and actually advocated for both homosexuals and transgender people to be accepted in society without treatment or incarceration. I'm not claiming that this was the case among the general public (Hirschfeld was beaten up in the 1920s, and when the Nazis came to power his whole library was burned), but Freud's view of homosexuality was similar to a lot of his contemporaries.

Source:

Robert A. Nye (ed.), Sexuality. Oxford: Oxford University Press, 1999.

Anna Clark, Desire: A History of European Sexuality. London and New York: Routledge, 2008.