In general, a person has an obligation to stop another person from doing something wrong as well as helping him to do something good and correct. Therefore, in theory, it would be the right thing to do to speak with the father. But it should be done in the proper manner.
You should not do it in a way that embarrasses the father in public. For example, if the scolding is over with, you could ask the father for a moment to speak privately. Of course, one should not do so if the father might be a violent person who could take offense and turn on you (or his son) if you try to offer constructive criticism, as nice and loving and unthreatening as you are. Even if the father is still scolding and publicly embarrassing his son, you can almost certainly find a way to kindly interrupt the scolding in a creative manner, followed by speaking to the father about how and hurtful and forbidden public embarrassment is.
Our Sages impress upon us how extremely wrong it is to embarrass another person in public. They teach, “Anyone who publicly embarrasses his companion is comparable to a shedder of blood.” (Tractate Bava Metzia 58b) A great Rabbi supported this teaching by an observation of human anatomy, when a person suffers great embarrassment “the red color of the face disappears, and it becomes white.” We see for ourselves that when a person is embarrassed his body reacts as if his blood has been drained.
The severity of embarrassing someone in public is so great, that on the Talmudic Sages also state that, “Anyone who publicly embarrasses his companion loses his portion in the World-to-Come”. And if that’s not enough, we are also taught, “It is better for a person to throw himself into a fiery furnace than to shame someone in public.” (Bava Metzia 59a)
Therefore, one should do the right thing and try to prevent others from causing public embarrassment or being embarrassed in public. It goes without saying that one’s own moral compass should certainly guide each person from this serious behavior, and always treat others with great respect and compassion.
