The reader gets a full explanation for Darcy’s behavior (in his own words) in his letter to Elizabeth in Chapter 22, which he gives her after she rejects his marriage proposal. In this explanatory letter, Darcy describes observing Jane and judging that she danced with Bingley “without any symptom of peculiar regard." He describes witnessing Bingley falling fast for Jane—as close friends, the two men know each other well, and Darcy therefore can tell that Bingley is in love.
Darcy then writes,
I remained convinced from the evening's scrutiny, that though she received his attentions with pleasure, she did not invite them by any participation of sentiment.
In other words, Darcy assumes Jane is not seriously interested in Bingley like he is in her. To protect his best friend’s feelings, he discourages Bingley from pursuing the relationship. He writes multiple paragraphs about his feelings toward Bingley and Jane’s relationship, telling Elizabeth that Bingley often looks to him for advice and that he felt a responsibility to share his opinion, despite not knowing Jane well.
In his letter, Darcy also explains that he objected to the Bennet family as suitable in-laws for Bingley:
The situation of your mother's family, though objectionable, was nothing in comparison of that total want of propriety so frequently, so almost uniformly, betrayed by herself, by your three younger sisters, and occasionally even by your father.
Darcy believes the Bennets (excepting Elizabeth and Jane) tend to demonstrate a lack of respectability. In the regency era, the upper class was was expected to be formal and reserved. The silly behavior of the younger Bennet girls and Mrs. Bennet's frequent boasting and outspoken desire for her daughters to marry advantageously fly in the face of the social conventions of the time. Indeed, Mrs. Bennet's behavior in particular motivates Darcy to separate Jane and Bingley, as her boasts lead him to fear that Jane is being pushed toward Mr. Bingley for his money.
Particularly in the beginning of the book, Darcy is reserved to the point of coldness; he has strict standards for his own and others’ behavior, and he finds Mrs. Bennet’s behavior (especially while observing her at the ball) offensive. Therefore, he sees Jane as an inappropriate match for Bingley, who might be embarrassed by in-laws who are so lacking in decorum. Darcy is incapable, at least in the beginning of the story, to look past the optics of Bingley and Jane’s relationship and perceive the genuine feelings on both sides. Undoubtably, his decision-making is influenced by the social code of the time, but Darcy also truly believes he’s looking out for his friend.