Why Apostolic Succession?

You'd have to ask the Apostles, as Francis Beckwith explicates.  Excerpts follow (much more at the original):

In 2007, when I was prayerfully thinking about returning to the Catholic Church, there were four theological issues that were deal breakers for me: justification, penance, transubstantiation, and apostolic succession. I have already discussed penance, transubstantiation, and justification. Here, I offer a brief account of how I became convinced that the Catholic Church is also right about apostolic succession.

Catholicism holds that if a Church claims to be Christian it must be able to show that its leaders – its bishops and its presbyters (or priests) – are successors of the Apostles. This is why the Catholic Church accepts Eastern Orthodox sacraments as legitimate even though the Orthodox are not in full communion with Rome.

What amazed me is how uncontroversial apostolic succession was in the Early Church, as Protestant historian J. N. D. Kelley points out in his book Early Christian Doctrines. I expected to find factions of Christians, including respected Church Fathers, who resisted episcopal ecclesiology. There aren’t any. In fact, a leading argument in the Early Church against heretics was their lack of episcopal lineage and continuity and thus their absence of communion with the visible and universal Church. In his famous apologetic treatise, Against Heresies (A.D. 182-188), St. Irenaeus (c. A.D. 140-202) makes that very point in several places. Tertullian (A.D. c. 160-220) offers the same sort of apologetic as well.

Of course, the very early Christians did not have the elaborate hierarchy and canon law of today’s Catholic Church. But they also lacked a secure and officially closed New Testament canon, conciliar approved creeds, a global Church with a global reach, and detailed and sophisticated articulations of the Trinity, the Incarnation, and justification. An infant Church is like a human infant. In its earliest stages it possesses in its essence properties that when fully mature are exemplified differently but are nevertheless rooted in the nature of the being itself.

So, the same human being who says, “Mama, me pooh-pooh,” may someday practice internal medicine. Thus, as the Church grows and develops, its intrinsic properties mature in order to accommodate its increasing membership as well as meet new theological, political, geographic, and pastoral challenges unanticipated by its younger incarnation...