In order for there to be attachment, you need two things -- the attacher, and the thing to which the attacher is attached. In other words, "attachment" requires self-reference, and it requires seeing the object of attachment as separate from oneself.
The Buddha taught that seeing oneself and everything else this way is a delusion. Further, it is a delusion that is the deepest cause of our unhappiness. It is because we mistakenly see ourselves as separate from everything else that we "attach."
We "pursue" happiness because we think it comes outside of ourselves. But it's also because we think things are outside of ourselves that we are stressed about them and worry about them. Whatever can be found can also be lost.
There's nothing wrong with striving to accomplish something, or making friends, or loving your spouse and children. The Buddha himself, after all, spent his life after his enlightenment associating with people, and teaching them. Non-attachment does not require extreme asceticism or shunning human contact. Non-attachment comes from the wisdom that nothing is truly separate.
The Buddha taught that craving grows from ignorance of the self. Because we see ourselves as something separate from everything else, we go through life grabbing one thing after another to ease our stress. We attach not only to physical things, but also to ideas and opinions about ourselves and the world around us. But physical things can be lost, and we get frustrated when the world doesn't conform to our ideas and opinions.
Extracts from 'About Buddhism'