I don't think there's anything you could have done better, in that setting.
Some of his points are legit. For example, Christians in recent centuries did own slaves, and I've seen patriarchy and misogyny even in modern Christians. There's a complicated conversation that one can have -- talking about how God reveals God's self in the context of different cultures, and how God seems to teach humankind in small steps, and how sometimes it's challenging for people to sort out which bits of early Christian practice were simply reflecting their culture's assumptions and which bits were direct teachings from God. But it requires a long span of time and patience to have that conversation -- maybe an hour, maybe multiple hours or more -- and it requires that both parties be ready to listen to each other with an open mind. A quick exchange on a street corner isn't going to be a good setting for a nuanced conversation.
What he doesn't say explicitly is that because you were standing at the entrance to a Pride festival, he may have assumed you were there to communicate an anti-gay message. If that's his perception, then that will tend to shut down the possibility of honest conversation. Perhaps a more neutral setting would be a more productive place for your message -- a table at a farmer's market or community fair, for example, where it's clear that you're not condemning the festival itself, but are just there to tell people that Jesus loves them and invites them into communion with him.
I'm pleased that you're going out into places where people are to meet people and tell them about your faith. It's easier, and more comfortable, to sit inside a church building and wait for people to come to us, but it's out in the world where we have the opportunities to listen to people's stories and minister to their needs.
