The eye contact made him very uncomfortable. He didn't want to tell Elijah anything, but he also didn't want to piss him off any more by doing so. So he was just basically being forced to either dump everything onto Elijah, or make up some random bullshit excuse. 

"I'm, just—" he couldn't find the words. There was so much he had to say, but he couldn't find the words to say any of it. And he also had to somehow figure out how to say it all without revealing that he knew things he wasn't supposed to know. Everything was horrible. "...would you miss me if I died?" That worked well enough. Probably gave Elijah an idea of what he's struggling with, which was enough.