The problem is how should he respond to that first question about kids? He can lie, and say that he doesn't have any, heading off the awkward situation, or he can tell the truth "yeah, I've got a couple of boys" or whatever. But if he tells the truth, he knows there's a good chance that he is going to get asked about his partner, and once again he has to decide whether he is going to lie or tell the truth.
The real problem comes from the fact that he is in the back of someone else's car, and he knows that violence against homosexuals is a depressingly common phenomenon. He doesn't know the driver, and hence can't know if they guy is going to be cool, or if he's going to decide that tonight's the night that he looks the passenger doors and drives off into the night to kill his passenger in some dark alleyway. Being less melodramatic, he could very easily find himself being dumped on the sidewalk halfway to his destination.
Hence the lies. But lies are tiring. You have to keep track of which ones you've told "Wait, did I just mention that I have to get up really early tomorrow to get the kids to school for a rehearsal? Damn - I told him I didn't have kids!" Anyway, that's what he's getting at.