While we're not treated to the details of Henry's proposal to Catherine, we are told that "Henry had saved her form the necessity of a conscientious rejection, by engaging her faith before he mentioned the subject [of his argument with his father]". I can only believe that it's true to what the narrator tells us - Henry is afraid that Catherine will turn him down if she knows that she's the source of a rift in the family - not that he's afraid Catherine will reject him if she knows he's fallen out with the General, for fear he'll be cut off. Henry knows Catherine for who she is, and it shows beautifully here.