Email is a vital conduit for human communication across businesses, organizations, and broader societal contexts. In this study, we aim to model the intents, expectations, and responsiveness in email exchanges. To this end, we release SIZZLER, a new dataset containing 1800 emails annotated with nuanced types of intents and expectations. We benchmark models ranging from feature-based logistic regression to zero-shot prompting of large language models. Leveraging the predictive model for intent, expectations, and 14 other features, we analyze 11.3M emails from GMANE to study how linguistic and social factors influence the conversational dynamics in email exchanges. Through our causal analysis, we find that the email response rates are influenced by social status, argumentation, and in certain limited contexts, the strength of social connection.