To put your question into context, we will first briefly discuss the rise of American industrialization.
The Industrial Revolution saw its emergence in America in the 19th Century. Prior to the early 19th century, much of American industry was concentrated in cottage productions. However, with the rise of mechanization came the standardization of tasks, the emergence of new factories, and unprecedented urban growth.
With the migration of more than eleven million people from rural areas to urban areas by the late 19th century, the American transformation from an agricultural-based economy to an industrial one was well on its way. The new textile, iron, and railroad industries changed the landscape of American business. The railroads allowed goods to be transported long distances across the continental United States. With new infrastructure in place, a new need for increased labor presented itself: millions of new immigrants from Europe poured into the United States in search of the same opportunities rural Americans sought in newly established, vibrant cities.
The profound change in the urban landscape was a result of the increased need for housing and industrial complexes. This left many Americans hungering for glimpses of a bygone era, where life was slower, calmer, and less confusing. More about this in James' novel below.
You can read more about American industrialization in the links below. It's great background for understanding Henry James' Washington Square.
In the midst of these developments on the national stage, Henry James pioneered a new psychological realism in his writings. He was interested in portraying the realities of a transforming America and in highlighting the effects of that transformation in the inner conflicts his characters experienced.
Henry James' Washington Square is no exception. Consider his description of what Dr. Sloper does for a living and where he chooses to live in New York City.
By the time the Doctor changed his residence the murmur of trade had become a mighty uproar, which was music in the ears of all good citizens interested in the commercial development, as they delighted to call it, of their fortunate isle. Dr. Sloper’s interest in this phenomenon was only indirect—though, seeing that, as the years went on, half his patients came to be overworked men of business, it might have been more immediate—and when most of his neighbours’ dwellings (also ornamented with granite copings and large fanlights) had been converted into offices, warehouses, and shipping agencies, and otherwise applied to the base uses of commerce, he determined to look out for a quieter home.
The above paragraphs present the new realities of American industrialization. Along with this mechanization emerged a concurrent predilection towards empiricism. Empiricism is largely concerned with quantifiable measures of data, so the conversion of homes for commercial purposes reinforces this new obsession with standardized labor and the mechanism of the corporate structure. One might say that the industrialists felt this would create a better society, but they didn't bargain for the human soul's thirst for meaning and substance.
The ideal of quiet and of genteel retirement, in 1835, was found in Washington Square...It has a kind of established repose which is not of frequent occurrence in other quarters of the long, shrill city; it has a riper, richer, more honourable look than any of the upper ramifications of the great longitudinal thoroughfare—the look of having had something of a social history.
These two paragraphs from Washington Square focus our attentions on the challenges of industrialization. Dr. Sloper's patients are mostly over-worked businessmen; he himself is loath to live in the ugly, exceptionally urbanized portions of New York City. Many like him hunger for the architectural beauties of a past era, replete with historical depth and character.
If you study Dr. Sloper's character, you come to recognize that his cold, analytical nature often manifests itself in almost deliberate cruelty towards his socially awkward daughter, Catherine. Dr. Sloper's incisive analysis of Morris' sham courtship of the hapless Catherine leads him to goad his daughter to despair regarding his observations. Dr. Sloper relies on observations and concrete data. He does his research regarding Morris' background. When he discovers that this black sheep is living off his sister, Mrs. Montgomery, he is scandalized.
He threatens to cut Catherine out of his will or to substantially reduce her share of his fortune if she decides to marry Morris. He is perturbed that Catherine cannot recognize the young man's avarice. Dr. Sloper is a metaphor for the dehumanizing influence of industrialization. He can't seem to translate the cold, hard facts he favors to any considerations towards his own child.
As a consequence, he fails to understand Catherine. Luckily for us, James' use of psychological realism allows us to understand Catherine for ourselves. His rich portrait of Catherine's inner conflicts, private cogitations, and personal fears causes us to sympathize with her plight as she navigates her path in life.
I hope the above has been helpful in some way!