Alternative approach: work backward from the product formula $C_2H_5NC$. In the carbylamine reaction, the carbon of the isocyanide's $-NC$ group comes from chloroform. Removing this $-NC$ unit leaves the alkyl fragment $C_2H_5-$, attached to nitrogen as $C_2H_5-NH_2$. Amino ethane matches exactly. Nitromethane and nitroethane are excluded because the carbylamine test only works on primary amines with a free $-NH_2$ group.