The Church is both Holy and sinful. How can it not be sinful, if it is composed entirely of sinners shepherded by a sinner and it's been like this ever since St. Peter?
And how can it not be Holy, if it's the original Apostolic Church, the very same organization, about which Christ said "the gates of Hell shall not overcome it".
We, no matter the vocation or position, are all sinners, it can not be any other way. But that doesn't mean the Apostolic Succession was ever in any way broken or misplaced. The Church is Holy in that it's dogma and doctrine are correct and it has legitimate claim of being the original church left on earth by the Apostles, the very people about whom the Gospels speak in their specific persons as the ones Christ himself sent away to teach all nations, the same who accompanied him intimately in the last three years of his time as one of Us. These people founded an organization headed by - on Jesus' explicit request, order and command - a sinner who denied his master, Peter. This organization is alive and more or less well and it is the Roman Catholic Church. It is as much the original Church as the original British Monarchy is the British Monarchy. These guys made a club and this club survived, it's structure, lineage, wisdom, everything the Holy Tradition consists of, are True and Correct in the most profound way.
At the same time the people who kept this Tradition and Teaching intact were susceptible to sin. How could it be any other way?
If you and eleven other guys are trusted to keep an Idea soundly intact because it's important, and I mean very, very important, you won't leave its safety to the general public, suspended in culture. You make a society, a community, whose members you task with preserving your Incredibly Important Idea. Idea like literal miracles happening, witnessed by thousands of people who've experienced Our Lord's supernatural miracles and who now, after His Passion and Death are left in sadness, terror and anger. Or perhaps just apathy.
You see the Miracle-maker who taught you for three years - the man you believe to be the God of Abraham Incarnate in a human body - risen from the dead in a god-like, transcendent form, exactly as he foretold. He tells you personally to make sure the things he said are kept and you make winnie the pooh sure the things he said are kept.
And if not sinners, who else? A Church led not by us but by will-less Magical Automatons from the Sky, incapable of wrong? Would you believe one of these guys if they went up a pulpit and told you to not sin? And how would faith? Wouldn't the existence of a measurably faultless being be supernatural itself and thus render faith invalid? Complete and utter absurd.
And why not leaderless and structureless? That doesn't work too, people always attain positions of power, some because of their pride and greed, other's to serve, the overwhelming majority because of some combination of these two.
Sinfulness of priests and truthfulness of the Word are not at all mutually exclusive.