The Buddha's first teaching gives us another approach to life, one that bypasses I/Not-I altogether: The Four Noble Truths. These truths tell us that suffering exists, it has a cause, it can be eradicated, and there is a path that leads to its eradication. But how does this give us a different approach to life? It instructs us to view all things, thoughts, actions, speech, not in terms of I/Not-I but in terms of suffering/not-suffering and cause/effect. This might seem like he was just swapping one dualistic viewpoint for another. But that's not the case. Thinking in terms of I/Not-I causes me to suffer: "That driver did something to me! How dare he!" "I didn't get that promotion, but Bill did. I'm a better [insert whatever quality you want here]
Thinking in terms of I/Not-I leaves us wide open to experiencing anger, jealousy or greed, and delusion. But the Buddha's approach gets us to focus directly on the problem at hand to eradicate the anger, the jealousy, the delusion, that is afflicting us. Instead of being angry at the other driver, we can recognize that anger has arisen and know that he had his reasons for his actions. We can sound our horn to let him know he should not have done that--maybe he did not even see us initially. But why cause ourselves to suffer (nobody likes being angry!)? Ultimately, we'd like to not react with anger, but with understanding and compassion (while still sounding our horn to let the other driver know of his mistake!). But if anger has arisen (suffering exists), we can know it has a cause (hint: it's NOT the other driver!). We can know there is a way to eradicate that response, and we can know the way to do so. The first and third truths comprise the suffering/not-suffering view, and the second and fourth truths comprise the cause/effect view.
In short, the Buddha gave us the means to directly face our suffering head-on and work directly to remove it, instead of the wallowing that occurs in the I/Not-I view.