Well yes I think he thinks that while people DO rise and fall in the social scale to an extent, generally speaking people stayed in the class they were born into... and if someone moves class, they may wind up feeling uncomfortable and not fitting in...
Robert is "rising" in the world, but probably HE wont be a gentleman, but maybe his sons may be, if he beocmes prospperous enough... and if Harriet were to think of herself as "a lady" and as such entitled ot marry soemone of Emma's class, she's likely to be disappointed in her expectations....