The Germany of the '20s was pretty desperate to feel good about themselves in some way. When WW I ended and all the Europeans wanted their "pound of flesh" to punish the aggressor, Germany was changed from a power base to a whipping dog. The payment of war debts crushed not only the government, but more importantly the people of Germany. They had no hope...so when an up and coming leader promises a return of Germany to prominence, the people - however slow or quickly - embraced it even though not all of the actions of the Nazi's were ethical or moral. Desperate people are willing to overlook a lot if it helps them to regain dignity, self-sufficiency, security, etc. The Nazi's were a political party, like any, that wanted to sway as many people to their ideology as they could. The problem was, that once they were in power, it became irreversible...like many so-called democracies today.
As for the youth being in the army and being allowed to go "off the leash", it is up to the leadership of any military force to establish discipline, morality, ethics, and conduct of its troops. The problem is morality, ethics, and conduct are subjective to the culture and circumstances of the populace of a country/region. Things that are horrendous to one culture may be widely acceptable to another.
The Goering grand-daughter...as many Germans shortly after the war...felt an undue responsibility towards its outcome. The guilt should be reserved for the leaders. I lived in Germany in early 2000's and even then, they still feel a guilt toward WW II and few will talk about it at any length. Most of the younger folks try to ignore it altogether it seemed.