This is a great question in an often overlooked scene. When we think of Juliet's progress through the play, we see a young woman who is incrementally let down by everyone who should be her support system. In the scene you mention, we see her father become cruel and tyrannical to her, where we had once thought him otherwise.
In this play, we find few villains, but there are many emotionally broken characters. Digging into the many ways the play hints at this opens the play to nuance. We learn early that Capulet married Juliet's mother when she too was very young—about Juliet's age. Their marriage was filled with multiple childbirths and only one surviving child, Juliet. Death hangs over this play in multiple ways.
We can imagine Lady Capulet felt traumatized by this too-early marriage and has learned to cope by shutting off much of her emotional life. She refuses to take Juliet's part, not because she disagrees with Juliet but because she is emotionally unable to access that empathy and plead with her husband for more time. No doubt, Lady Capulet has rarely crossed her husband's will.
Lord Capulet is a pleasant enough man who is used to having his way, and he has largely been rewarded for it. As he considers Juliet's marriage, he is excited that his family will be making a social move upwards by marrying Juliet to the Count. One senses that the work of his life has been to groom her and the family name for such a socially aspirational move. Juliet's refusal to marry opposes Lord Capulet's entire plan for her life and for the family's name. In rejecting his choice in marriage, Juliet presents a dangerous threat to all he has worked for.
When Juliet's parents find her "dead" on her wedding morning, we may rightly be struck by the seemingly cliche words of grief. This seems an intentionally awkward scene compared to Juliet's earlier authenticity. One senses that the Capulet parents have both learned to distance themselves from a reflective inner life as well as from a habit of attention to others that Shakespeare so often says is essential in a well-lived human experience.