Perhaps there is so much discussion because there is no hard and fast rule for this, and each family is different both in make-up and temperment. But looking at some of the guidance the Church has given will help us to see how to proceed in a way that is right for our own family.
First let’s see what Canon Law says:
Canon11: Merely ecclesiastical laws bind those who have been baptized in the Catholic Church or received into it, possess the efficient use of reason, and, unless the law expressly provides otherwise, have completed seven years of age.
So there is no obligation on the child’s part to go until age of reason and completion of his seventh year.
But, by their baptism, children have certain rights:
Canon 217: Since they are called by baptism to lead a life in keeping with the teaching of the gospel, the Christian faithful have the right to a Christian education by which they are to be instructed properly to strive for the maturity of the human person and at the same time to know and live the mystery of salvation.
Parents have an obligation to the children:
Can. 226 §1. According to their own vocation, those who live in the marital state are bound by a special duty to work through marriage and the family to build up the people of God.
§2. Since they have given life to their children, parents have a most grave obligation and possess the right to educate them. Therefore, it is for Christian parents particularly to take care of the Christian education of their children according to the doctrine handed on by the Church
So, it is the primary obligation of the parents to educate their children in the faith and prepare them for a Eucharistic life, and it is the children’s right to receive this education. Obviously, before the Sunday obligation takes effect for the child, you want him to already be participating regularly in the Eucharistic celebration to the extent that he is able. How this is accomplished in each family will vary.
From day one, and especially from the time they are baptized, it is totally appropriate that children be included in the Eucharistic Celebration. Yet not all children are ready or willing. In the meantime, the parents will hopefully be praying for and with their children, and be preparing them for regular Mass attendance.
Many parents with infants find it very difficult to bring them to Mass, especially if a toddler is also in tow. A single parent will find this especially difficult. But the goal is to get them coming as soon as they are able, and if they are not able to yet, get them ready by familiarizing them with the Church as often as possible, maybe for short visits and gradually extending those visits. Going to Church should be a privledge and something they want to do.
While children cannot fully understand all that goes on at Mass, they can still participate in some ways. They can learn to genuflect and bow. They can assist in taking the gifts up. They can place the envelope in the basket, or have their own contribution to offer. They can sing, and the family can reinforce these songs at home. If the Our Father is said regularly at home, then they will look forward to saying it. The same holds true for the sign of peace.
(See below for a continuation of this answer)