The idea of waiting after eating meat before enjoying dairy again, is rabbinic. The Torah does not give such instructions which is why there are different amounts of waiting time in different places.
The Dutch only wait an hour and the German Jews three hours. This is based on a Tosfot in חולין that says one must wait the average time between meals. It was assumed that the Dutch eat several small meals in the course of the day.
There is a מחלוקת ראשונים that is widely accepted as the reason to wait six hours. One opinion is based on a Pasuk והבשר עודנו בין השיניים that the meat was between their teeth ( referring to the quails). It takes six hours for food to get dislodged from between the teeth.
The other opinion was that it takes six hours for food to be digested. The difference between the two reasons applied to mothers who used to chew the food for their young children with no teeth to soften it. (Before Gerber's) According to the opinion of digestion, the mother would not be בשרי. According to the opinion of food between the teeth, she would have to wait six hours.