I reckon that thinking of aspects as “positive” or “negative” is a bit of a misnomer, although it's not entirely incorrect. It's better, IMO, to think in terms of spending and receiving fate points, as well as story contracts. Brett describes aspects as a contract with the GM, and the other players, for certain types of gameplay (either styles of adventures that might happen, or the sorts of things your character is known to do). It's worth keeping that in mind.
The best aspects allow all three, but most aspects should at least do two, IMO. That said, you definitely do want to make sure that you have aspects that gain you fate points, as well as aspects to spend them on, but these aren't necessarily mutually exclusive sets, if you follow me.
Have you read Brett's long email on what Fate points can be used for?
Generally speaking, Aspects which get you fate points imply actions or situations which complicate matters for the character. (This is a bit more general than just things with are flat out bad or undesirable). Aspects which you spend points on will generally either give you some advantage somewhere, or give you some control over the game through declarations.
A good example, I think, is “The Favour Economy” aspect that one of my characters in another game has. This is general-purpose. It allows me to spend a fate point to declare either that an NPC owes me a favour, or to make up and introduce an NPC that owes me a favour. The GM may invoke it (thus giving me a fate point) to declare that I own a particular NPC a favour. Other players can tag it to get me to do something I don't want to do, by declaring that they'll owe me a favour if I do. On top of all that, it lets the GM and the players know that I expect the dealing of favours to be a thing which might be a part of stories we're playing (and furthermore that it ought to be used in at lease some of them).
If you have a look at Brett's character from the same game, he's done a very nice analysis of his aspects including how he intends for them to be used. I think it's very illustrative of the general concept.
I hope this is a little helpful.