
In Reveng of the Sith, Anakin begins having disturbing dreams about Padme, like the ones he had about his mother before she died.
First, let's compare the two situations.
In Episode II: Anakin is with Padme, falling in love and enjoying life, etc, when he has bad dreams about his mother in pain. They are so great, and he cares for his mother so much, that he eventually finds it impossible to not seek her out to save her. He travels to Tatooine and tracks her down, and along the way travels down the saddest and most angry path he ever has, and come closer to the dark side than he ever had before up to that point.
In Episode III: He's been a good Jedi. He's not perfect, he killed an unarmed prisoner, but only on the order of ruler of the Galaxy and Lord of the Sith, and not wihout hesitation or guilt. But he's been generally good. Then he has these dreams. We know where it takes him, and this premonition is the most key peice in his submission to Sidious as Master, and it leads him to fall as far as he can. What's different about this dream is that he remembers his other dream about his mother, and sees it's significance and takes it even more seriously, seeking Yoda himself for counsel on the matter.
It is interesting, how the two darkest events in Anakin's life are both forseen in his dreams. They are so parrallel. Two women, two dreams of them suffering, and temptation and anger when he reaches the end each path.
Both dreams are similar, and both eventually corrupt Anakin to a point where the Dark Side is the only tool for doing what he thinks he must.
Now what does Yoda have to say about this?
"Careful you must be when sensing the future, Anakin. The fear of loss is the path to the Dark Side."
Right off the bat, Yoda gets staight to the crux of the issue. Good job, Yoda. These examples of Anakin's dreams, and the feelings he feels as a result, are the ideal proof of this statement. The fear of loss is exactly what brings Anakin to abandon the Jedi teachings, through these events.
Anakin responds
"I won't let these visions come true, master Yoda"
Already he is unwilling to accept loss.
"Death is a natural part of life. Rejoice for those around you who have transformed into the force. Mourn them do not. Miss them do not."
Yoda is trying to teach Anakin why he should not be so occupied with the death of those he cares for. In terms of the Force, death means very little. It is important for a Jedi to not become obsessed with emotions about death, or anything, because...
"Attachment leads to jealousy. The shadow of greed, that is."
Greed and jealously are not really Anakin's problem in this case, but this is a great example of one of the many principles for restricting emotions that the Jedi must maintain.Yo be a Jedi is to walk a fine line, always wary of temptation and passion. This leads to a very potent point about the ways and teachings of the Jedi, and how they are forced to live. Jedi must detach themselves from many things, including emotions. Because a Jedi is strong in the Force, the danger of the Dark Side tapping into their negative emotions is great, and must constantly be gaurded against.
The best way to do this, or so the Jedi of the Old Jedi Order believe, is to isolate their life from certain things that inspire temptations and negative emotions. That is why the lives of Jedi are largely void of material possessions, why Jedi are not allowed to love, and exactly why it is an important Jedi teaching to consider death favorably and peacefully, for if Jedi took deaths too seriously, the emotional disturbances and repurcussions would be disastrous. Revenge alone is too powerful an emotion and too great a tool of the Dark Side to leave unchecked in jedi teachings, and revenge may be just one of many strong emotion spurred by death.
"Train yourself to let go of everything you fear to lose."
This is the simple how. How to save yourself from emotional turmoil over loss. A Jedi must detach themself from a lot of things, inorder to maintain a peaceful disposition.
And more importantly, this is exactly what Anakin cannot do. He is unable to simply let go of those he cares for for his duties as a Jedi. He doesn't value the way of the Jedi enough to overcome the strong feelings he has for his mother and for Padme.
The fact about Anakin that tipped the scale for him to fall, rather than stay the path of Light was that in the end, he cared more about his loved ones than he did the ways of the Jedi. He never fully accepted some of the Jedi teachings, such as these crucial ones Yoda wisely dictates. He hasn't truly learned those lessons, and submitted to the temptations that those teachings were meant to gaurd against. When the time to make the choice came, he chose the path of Dark for the sake of the women he loved.
There are several ways to consider that though. He cared for Padme more than the Jedi, but was it because he didn't care much for the Jedi? or because he cares so much for Padme? Was this because of his late start in training and deep emotionaly connection with his mother? Or was it a failing of his teachers? Or perhaps it was simply his nature. Those are important to think about and discuss, as the deepest motivations for Anakin's stance on these issues are the true keys to why he fell.