The swastika is a symbol that goes back a long way in history and is most commonly known as a symbol of Hinduism, Buddhism, and the Nazi party. Of course, the Nazi party was not really anything to do with the culture that used the swastika for thousands of years before them.
The swastika is a symbol which has only recently become a symbol of hate, at least in terms of the amount of time it has existed in society.
In Buddhism and Hinduism, it is known as a symbol of good luck, perhaps representing eternity, or the two different types of forces in the endless cycle of death and rebirth called Samsara.
There is the right facing swastika, or the one highjacked by the Nazi party, which represents the evolution of the universe (pravritti), and the left-facing swastika, which symbolizes the involution of the universe (Nivritti, the process that allows creation to happen).
The left facing swastika is most commonly known as a symbol of Buddhism, and is used on maps to indicate a Buddhist temple, and the symbol is still found on many ancient temples, and other works of art.
What were the reasons behind the Nazis using the well known symbol from Hinduism and Buddhism? Did Hitler actually understand what it meant?
The real question is, did Hitler and the Nazi party use the symbol because it looked good, or were they actually somewhat religious? Was Hitler really a strongly Christian man like he claimed to be, or was it just a pre-text for inciting the hate necessary to start a war for world conquest?
It seems strange that Japan was their ally in the war, (a mostly Buddhist country), if they were actually seeking to discredit Buddhism.
The history of the term Aryan goes back to ancient times when there was a similar "master race" from south Russia who invaded India, Iran, and many of the countries of Asia and Europe that surrounded them.
Regardless of the causes of world war two, and the suffering caused by Hitler's quest for world domination, the Nazi symbol is still quite important to many cultures, where it represents something completely different.
You could not possibly get more of a difference in world view between the Nazis and the Buddhist monks. In terms of history, the Buddhists and Hindus have more claim on the symbol than the short-lived Nazi party, and that's why in Germany, the swastika is allowed only in religious circumstances.
The left facing swastika is the sign of Buddhism, which makes Hitler's right facing swastika seem almost like a pentagram, or a cross turned upside down, although you cannot have life without evolution.