If you are really serious about reaching out to homosexuals this 2011 article in from the New Oxford Review by Melinda Selmys is a good way to start thinking about it.
I was converted, not by arguments against homosexuality, but by the love of Christ. I was aware of the arguments years before I converted and even found them relatively coherent. I could see that if you believed in a God who had designed the universe, and that the natural creation was a manifestation of His wisdom, and that sexuality was ordered and designed for the union of spouses and the procreation of children, then obviously homosexuality had to be immoral. I didn’t believe in such a God. Nor would I have been willing to give up one of the most important relationships in my life for anything less than the person of Christ Himself.
Effective outreach to the homosexual community will be possible only when Catholics are willing to acknowledge that there are real reasons why gays and lesbians choose to identify with their sexuality and that these reasons have to do with more than just sex. Only then can authentic and fruitful dialogue take place. It is not enough to offer arguments, however rational, against the morality of homosexual acts. If the Church does not offer adequate emotional and spiritual support for people with same-sex attractions who wish to live out a full Catholic life in accord with magisterial teaching, then Catholic witness is doomed to failure. A small minority will be willing to tough it out, but the vast majority will turn to the gay subculture and the LGBTQ community, where there is at least a strong and concerted effort to see that their emotional needs are being met.
It is also essential that Catholics enter into this dialogue with humility, and recognize that our own attitudes, and the attitudes expressed by Christians in the past, have caused real and substantial harm to people with same-sex attractions. Often the simple acknowledgment of another person’s grievances, and the willingness to listen and to respond with compassion and contrition, is enough to break down the barriers that prevent real understanding.