star wars - SW prequel Yoda: "Attachment leads to jealousy, the shadow of greed, that is". What does this line mean?

In Star Wars Episode 3, Revenge of the Sith, there's a scene where Anakin and Yoda are sitting in that little meditation room (with the horizontal shades over the windows) and discussing the meaning of Anakin's recent premonitions of "someone" (Padme) dying. Yoda gives Anakin a piece of advice that starts out quite wise, but then, for me, skews off into nonsense.

Yoda: "These visions you have ..."

Anakin: "They are of pain, suffering ... death."

...

Yoda: "Careful you must be when sensing the future, Anakin! The fear of loss is a path to the Dark Side."

Anakin: "I won't let my visions come true, Master Yoda."

Yoda: "Rejoice for those around us who transform into the Force. Mourn them, do not. Miss them, do not. Attachment leads to jealousy, the shadow of greed, that is."

Anakin: "What must I do, Master Yoda?"

Yoda: "Train yourself to let go of everything you fear to lose."

The bold words are the parts that I find to make little sense or have little relevance to the problem Anakin is trying to seek help for.

Now, I understand that certain George-Lucas-isms have been injected into this speech, but maybe I'm the one who just fails to understand the meaning?

First of all, how is fearing for a loved one a path to evil? Isn't that precisely what makes a tragic hero tragic? It may be harkening back to the Phantom Menace's "Fear leads to anger, anger leads to hate, hate leads to suffering" line, but even that is gibberish.

My biggest problem is the "attachment leads to jealousy" line. Now, I've put a LOT of thought into trying to understand this, but I've come up empty each time. According to Lucas, the Jedi are similar to Buddhist monks, so I looked up "attachment in Buddhism" and discovered that it means something very different to the Western world's definition of attachment.

We Westerners see 'attachment' as synonymous to a bond, a relationship or even love. Buddhism defines it as ... well, something confusing to me. One definition is that it is "clinging", another, that it is "craving" and then another that says something about "becoming" ... I have no good idea what any of this means or how it relates to Anakin Skywalker, or greed, or jealousy.

Then there's the "letting go of what you fear to lose" part. This sounds, a lot, like Yoda is saying, "Well, Anakin, to spare yourself the pain of grief, you should just cut this person out of your life and forget them. Let them go before he/she dies!" I would assume that he means to learn to let Padme go after she dies, but the wording of "train yourself to let go of everything you fear to lose" is so darn vague and sounds like Yoda is talking about "letting go" while Padme is still alive. Isn't that a little cold?

Does anyone know what is going on in this scene? :P