Second try

async.py

class Authenticator:
    def __init__(self, sock):
        self.sock = sock
        self.login = None
        self.pass = None
        self.to_send = "LOGIN"
        self.to_read = None

    def on_write(self):
        if self.to_send == "LOGIN":
            self.to_read = "LOGIN"
        elif self.to_send == "PASS":
            self.to_read = "PASS"

        self.sock.send(self.to_send)
        self.to_send = None

    def on_read(self):
        data = self.sock.recv(2 ** 10)
        if self.to_read == ...

        self.to_read = None