Node.js heavily uses an event-driven architecture, particularly for asynchronous operations like starting a server. The EventEmitter class is the foundation for this pattern. Objects that are event emitters, like the server object described, use the .on(eventName, listener) method to register a callback function (the listener) that executes when a specific event is emitted. The conventional name for error events is 'error'. Therefore, server.on('error', callback) is the standard, idiomatic way to listen for and handle asynchronous errors from such an object.

A. server.error() is not a standard method in the Node.js EventEmitter API for registering an error listener.

B. server.catch() is the syntax for handling rejected Promises. The question specifies the library uses "events and callbacks," not Promises.

C. try...catch blocks only handle synchronous errors. An error during server boot-up (e.g., port in use) is typically an asynchronous event and would not be caught by this block.

1. Node.js Official Documentation, events module. The documentation clearly shows that emitter.on(eventName, listener) is the method to add a listener function for a named event.

2. Node.js Official Documentation, Error Handling. The section on Error Events states, "When an asynchronous method has an error, the error is passed to the callback... For EventEmitter classes, errors are routed to the 'error' event."