For several moments, he did not respond, even to acknowledge Arcturus' vow of secrecy. Antonin was mentally and physically bracing himself for his confession, not because he was ashamed. If being inside an enclosed space like a carriage was enough to cause a negative reaction, what would it be like to actually discuss his experience?
"You are young, but no doubt you have heard of Azkaban? My illness stems from being imprisoned there for over a year. The Dementors have taken their toll, and chocolate is the only remedy to overcome their joy-draining effects upon my soul."