Development vs. QA - Why disagree?

We tend to see testing categorized as two extremes: 1. On one side, you have QA testing oriented around testing business requirements and the end-user experience. This is often accomplished by testing a finished user interface. 2. Developer testing is gaining prominence over the past 3-5 years. There is some value to improving the quality of developer code, and using unit tests to develop iteratively. But it seems like developers are increasingly expected to test their own code WHILE they are developing it. So in this topic, let's cover the real questions that both sides of the house face, and try to answer:

1. Why can’t we live in harmony and prevent the adversarial approach to testing? Especially if we all have the same goal in mind?
2. What are the differences between QA and Dev testing approaches?
3. What are the strengths and weaknesses of each type of testing?
4. How can the two groups work together better?

As always, your opinions matter and we'll jump in.