Being loyal to one's family was still a crucial cardinal value in Henry's time. This is one reason Catherine does not expect him to confront his father and why (as you say) the break with the General is so dramatic.

How Henry would think, and feel, and look, when he returned on the morrow to Northanger and heard of her being gone, was a question of force and interest to rise over every other, to be never ceasing, alternately irritating and soothing; it sometimes suggested the dread of his calm acquiescence, and at others was answered by the sweetest confidence in his regret and resentment. To the general, of course, he would not dare to speak; but to Eleanor — what might he not say to Eleanor about her? (Ch. 29)

This is also why Eleanor was so tongue-tied when telling Catherine of her dismissal from the Abbey; she felt herself duty-bound not to speak ill of her father even though she found his actions horrifying.

Henry owes loyalty to his brother and sister as well as his father. One of Thorpe's failings is that he so often denigrates his family.