Each of the sacraments has its own unique requirements for validity. Essentially, God has promised us that He will act in a certain way when we do certain things, so that we can have confidence in our justification and spiritual life.
In baptism, what is required is that water be passed over the baptized person’s head, that the baptism be in the name of the Father and of the Son and of the Holy Spirit, and that the person doing the baptizing intend to do what the Church does when she baptizes. These elements are present in the baptisms of most self-described Christians.
In the Eucharist, what is required is that wheat bread and grape wine be consecrated in connection to Christ’s words “this is my body” and “this is the chalice of my blood”, that the person doing the consecration be a validly ordained Christian priest (that would include validly ordained bishops, of course), and that the priest intend to do what the Church does when the Eucharistic elements are consecrated.
Now, the problem with the Anglican eucharist is not their eucharistic celebrations, but their ordinations.
For ordination to the priesthood to be valid, what is required is that the person being ordained be a validly baptized male, that the person doing the ordination be a validly ordained bishop, the laying of the bishop’s hands on the man being ordained, and the intention on the part of the bishop to do what the Church does when she ordains priests, an essential element of which is the intention to ordain them to a sacrificial ministry.
It’s that last bit that’s the source of the problem for Anglicans. Though a sacrificial theology of the Eucharist has been revived in some corners of Anglicanism in the last century and a half, for the most part and for most of Anglican history Anglican presbyters, who before the mid-19th century were, I believe, generally called parsons rather than priests, were not thought of as offering a sacrifice when they celebrated the Eucharist. That means that the ministry to which they were being ordained was not that of a priest who offers sacrifice, and so the Catholic Church considers the ordinations performed with that deficient intention invalid.
Today, of course, some Anglican bishops do likely think of themselves as ordaining men to a sacrificial priesthood, but after several centuries in which this theology was absent from Anglicanism, the chain of Apostolic succession has been broken. Thus the requirement than the man doing the ordaining be a validly ordained bishop is not met. If there is no validly ordained bishop to do the ordinations, then no ordination will take place even if the man attempting to ordain has the right intention.
Or, at the very least, we cannot have any confidence an ordination will take place, because the conditions God has set in guaranteeing his action have not been met. Theoretically at least, God could still act. He, for His part, is not bound by the requirements He has set for the sacraments. But we have no assurance from Him of how He will act in a case such as this, and so we can’t presume He’ll make an exception.
