As Reeba has explained very well, this long trip to Cleveland is all about Willoughby trying to vindicate himself in the eyes of Marianne and Elinor, even if that comes at the expense of Col. Brandon, Eliza, Mrs. Smith, his wife (the former Miss Grey), Sir John Middleton, etc. Essentially, Willoughby cannot bear the idea that the Dashwoods might (justly) think poorly of him, and perhaps he does not want Marianne to die thinking the very worst of him. Making a genuine apology for the hurt he has caused and taking responsibility for his actions do not seem to be his objectives here.