I thought that this was the primary point of Henry's analogy - that he should not have to share his partner with a disengaged man. Of course, in marriage that was a man's legal right, but a dance partner has no right to demand who his lady can or cannot talk to. I am not sure if he is showing a decided preference for Catherine's society or merely for the lack of John Thorpe's, but isn't he clever, to make his wishes known to Catherine in such a delicious, flattering and gentle way? (much better than coming to blows with John Thorpe then demanding satisfaction for his ladies honour- when I read this chapter I can see why this sort of behavior was popular. Poor Catherine, obliged to dance with John Thorpe or not at all!)

I doubt Henry is speaking improperly -- "The advantages of Bath to the young are pretty generally understood." as Mrs Elton delicately put it, in Emma; andas far as I can gauge Cathrine's understanding of his speech, she is not offended.

What I am enjoying, is the complete naivety of the Morelands - Catherine is as bewildered by Henry's pleasantries as Jomes was by the manner in which Isabella accepts him for a second dance in chapter eight. The Morelands seem flat-footed in the social whirl of Bath.
And Mrs Allen is woefully deficient as a gothic heroines duenna - even if she is able to tell which of the young men is so charming, her attempts at gathering gossip about the Tilneys leave something to be desired.

One thing that I am not sure of, is what John Thorpe means when he calls his sisters 'quizzers' -- does he mean they are expert in making fun of eccentric people, or that they are eccentric people and fair game for making fun of?
There is no mention of the term in Dr Johnson's dictionary, and while I found the definition below at thefreedictionary.com, it doesn't really solve my puzzle.

quizzer n.
Word History: The origins of the word quiz are as difficult to pin down as the answers to some quizzes. We can say that its first recorded sense has to do with people, not tests. The term, first recorded in 1782, meant "an odd or eccentric person." From the noun in this sense came a verb meaning "to make sport or fun of" and "to regard mockingly." In English dialects and probably in American English the verb quiz acquired senses relating to interrogation and questioning. This presumably occurred because quiz was associated with question, inquisitive, or perhaps the English dialect verb quiset, "to question" (probably itself short for obsolete inquisite, "to investigate"). From this new area of meaning came the noun and verb senses all too familiar to students. The second recorded instance of the noun sense occurs in the writings of no less an educator than William James, who in a December 26, 1867, letter proffers the hope that "perhaps giving 'quizzes' in anatomy and physiology . . . may help along."