Zach took offense at the idea he couldn't keep a secret. He most definitely could, as evidenced by the fact his very own mentor had not suspected anything of him until the damn veela had to come along and ruin his cover. And even then, only T had figured out there was something to figure out.
Zach just liked knowing the secrets. That was all. "I can take secrets to my grave," Zacharias disagreed. He sat straight up, with excellent posture. He had always been that way, once he had gotten to interact with people and became aware of the idea of secrets.
"Come on, you can try me," Zach offered, "Tell me a secret you don't want anyone to know, and I will take it to my grave." He held his hand across his heart.