If a Catholic couple marry themselves, why did the Vatican object to the SSPX marrying people?

First, couples do not marry themselves. They give themselves in vows because the Church requires them to, but what makes it a legal, binding union is the Church, the only legal entity that can join them together. When the priest says 'I now pronounce you man and wife,' that is a legal statement by a legal authority; the bond depends on the Church, not on the couple. As for the SSPX: when they began under Archbishop Lefebvre, they did not start as an organization that would produce its own priests and marry its own people. They functioned under the bishop, and their priests were being formed for the bishop's diocese, not for the SSPX itself. So they were never given the privilege to marry people as the SSPX; if a bishop gave an SSPX priest authority to marry, it was because the couple were in that bishop's diocese and the priest was doing a service for the bishop, and that couple remained under the bishop. The idea that the SSPX was an independent organization is wrong, and it has confused many people. Over time the SSPX assumed all these functions on its own authority, apart from the bishop, and if they now treat the marriages they perform as their own, they will also have to create their own tribunals to judge annulments and divorces, exactly what the Church has always had, authority they were never meant to have. When they started in the 1960s they were given a six-year trial period, and Archbishop Lefebvre agreed to it; whether they would remain was in the hands of the bishop, or even the pope. Every finger Lefebvre pointed at the wayward Vatican church was probably right, but his reaction went in the wrong direction. The doctrine of the Church's authority as a canonical, legal entity before God is just as important as her theological and moral doctrine; you cannot let the doctrine go astray and then use that as an excuse to disobey the Church's authority and effectively create a new church. None of the infallible doctrines have changed, so the Church is still indefectible, but that requires the authoritative Church still standing, no matter how many barnacles are on it. Only Jesus Christ can take it away, and so far He has chosen not to. Read the Old Testament: God let Israel go on through twenty bad kings in the northern kingdom before finally dispersing them in 722 BC; He kept the structure, warned them again and again, and only then lowered the boom. We are just like them, and God is keeping the structure of the Church the same way until He alone decides to act.