It all depends how you define left and right. It isn't just one thing that differentiates them. There's a whole host of things that can be called "left" or "right".
I think the main difference between the left and the right however, has more to do with how they try to achieve their ends than with what they actually argue for. The left tends to favour progressive change, while the right tends to be more conservative or favour extremely slow change. As you get further left you get more and more progressive until revolution is espoused. This view of the spectrum has its origins in the French Revolution; the divide originated there, when the conservative, monarch supporters sat to the right and those who favoured change sat to the left.
As different issues have popped up over time, the case has almost always been that those who took the progressive stance have been labelled left.
Consider homosexuality: those who want to institute same-sex marriage are usually leftists while those who want marriage to remain traditional are conservative rightists.
You can also notice that different views change their position over time. Once upon a time, racism was a centrist value. Most people supported it as a "normal" value. Then, some people argued that it was wrong. This would have been a left position at the time. Over time, that position became more acceptable. Now, anti-racism is considered centrist ("normal") while those who continue to support it are considered particularly conservative, maybe even extremely so. Once upon a time, laissez-faire capitalism was extremely left wing, opposed by the aristocracy. Now, its considered to the right, and I think absolute monarchy/aristocracy has fallen off the right edge of the spectrum completely.
Thus, even though many things characterise the left-right divide, I think the committment to change/method of change covers the most paradigms and is the best explanation. However, even this has its problems and is not a perfect analysis.
That's why fascism is so difficult to define. It is quite revolutionary, seeking rapid and violent change to the existing order, but in order for (mostly) conservative values to be reinforced, or in some cases, reinstituted. It's difficult to place it on the spectrum.
It seeks an overthrow to the existing order, like communism, but wants this existing order to be characterised by traditionally conservative values, such as nationalism, sexism, anti-homosexual sentiments and statism. It will support capitalism, but only if the state benefits from it. Think about it; capitalism is OK; but not for the "people", or for "freedom", or for "individualism", but for the country. At the same time, these views are to be realised through radical change, not reform or conservatism.
So it can be said that fascism is a mix of left and right; it advocates traditionally conservative/reactionary policies but through revolutionary means. The reason it has been defined as far right is probably because of the character of the views themselves, ignoring the way they might be realised. The fact that fascists/nazis made most of their political alliances with other, more traditional right parties, and virulently opposed communism and the left, probably made this analysis easier to justify.
Sorry for the long post.
