The simple answer is that it would ensure fairness to all parties, no one point of view would be held above the others. There were different political parties that made up the government, and they had different ideals, so were conservative, others were not, some wanted a lot of government involvement and the others didn't want a lot of government involvement. If all these different groups, representing the majority of the people, did not have an equal say in the writing of the constitution, the document would have ended up favoring certain groups and pushing the others to the wayside.
It would be like having a school of blacks, white, Hispanics, gay, straights, transgenders, cisgenders, Christians, Muslims, Buddhists, Hindus, jocks, nerds, and creative kids. Now, this school wants to decide on a new dress code, rules on behaviors/speech, and changes to the types of classes offered. Now imagine they only chose to ask the students who were cisgender, straight, white, christian, and jocks. These students would choose things that fit with their ideals and preferences, but the policies meant for the whole school would only benefit them and not the rest of the population.
Make sense?
