Indeed, there are some mission presidents who turn out to be real lemons. The most infamous example I'm aware of is that of Delbert Groberg, who ran the Tokyo South Mission from 1979-82. You have to read the entire thread to believe it; although presented through an anti-Mormon filter, the facts are plain to see. He basically ran the mission like it was an antebellum Southern plantation.
However, a bad mission experience does not need to lead to apostasy, and the majority of missionaries do recover and remain with the Church. One such person is Ardis Parshall, who edits the Keepapitchinin blog, which specializes in Mormon history. Sister Parshall had a bad missionary experience because of a mission president who didn't like sister missionaries. Here's part of her description:
I’ve mentioned before that my mission was a disaster. That wasn’t because I wasn’t a good missionary, or because I didn’t work hard, or because I didn’t follow the rules. I was, and I did, and I did. My mission was a disaster because my second mission president was a disaster, a man who should never have been a mission president, or at least should never have had sister missionaries placed within his stewardship. This was a man whose very first words to me were “I don’t like you,” and whose every word and action after that was dedicated to proving that he meant what he said. If there was a way he could abuse me, he found a way to do it, in words, in deeds, emotionally, spiritually, physically, verbally. There was even a definite sexual aspect to some of his abuse, although I do not mean to suggest that he ever touched me in that way; he did not. But that’s about all he didn’t do.
Sister Parshall notes that this experience tested her faith almost to the limits. She began to doubt the existence of God and the veracity of the Church. She just could not understand why God would call a man like that to be her mission president. But she previously had a manifestation in which she literally heard the voice of the Savior Himself, which prevented her from losing her testimony altogether. Several years later, Sister Parshall finally figured it out:
I gradually came to understand that while men could be and should be and more often than not are called of God, men do not always live up to their callings. One man’s failure to live up to his calling does not invalidate the call, nor the God or the Church leader that extended the call. Such a man will have to answer some day for his failings, just as I will have to answer for mine; in the meantime, I don’t have to worry about it anymore. It seems so obvious now that it’s hard for me to understand why it took me so long to reach that understanding. But it did, and I do understand.
As a result, her testimony is now rock-solid, and most importantly, none of the idiosyncracies of Mormon history causes her the least amount of stress. Many people encounter contrasting accounts of Church history, and because they can't reconcile it with more official accounts, decide the whole Church is a crock and bail out. The fact is, history is written by different people with variable agendas and multiple perspectives; there will be differences.
But it does NOT need to lead to apostasy. Ardis Parshall is proof, as are the thousands of former missionaries who remain faithful and build successful lives and families. There's also another reason why one man’s failure to live up to his calling does not invalidate the call, nor the God or the Church leader that extended the call. The Second Article of Faith gives us a lifeline:
"We believe that men will be punished for their own sins, and not for Adam’s transgression".
While intended primarily to rebut the traditional Christian doctrine of original sin, by extension this article of faith implies we are responsible for nobody's sins except our own. So if Joseph Smith or Brigham Young sinned, that's not our problem, because we don't have to answer for their sins. Likewise, we won't have to apologize for our Church's history, not only because those of us who are alive today did not make that history, but also because the Church has taken steps to mitigate the unfortunate parts. We've properly memorialized the victims of the Mountain Meadows Massacre. And we extended the Priesthood to all worthy males in 1978. Furthermore, we believe that worthy Black men who were denied the Priesthood in this life through no fault of their own will get the opportunity to accept it in the spirit world; we do their temple work daily in case they want to take advantage of it.
We have nothing to apologize for as Latter-day Saints -- except our own failures today. So our history is no excuse for apostasy. And neither is a bad mission president. If Ardis Parshall can overcome, so can anyone else.