You do understand that eye for an eye was a determination of the punishment for particular crimes. If someone committed a crime of hurting someone, the punishment meted out by the authorities should match the crime. So, an eye for an eye.
Turn the other cheek was not about punishment for a crime. It was about how we as individuals should approach persecution or difficulty with others in particular authority.
It seems the reason you have so much trouble debating these homosexuals is that you yourself don’t know the Bible as well as you could.
I suggest you do more study and invite the Holy Spirit and more Bible literate Christians to guide you.
Well, I’m not actually debating the pro gay people yet — I’m preparing for it — and you are right that I don’t know the Bible that well. Actually, the course I’m taking is an introduction to Bible Studies.