Science by definition can provide, in principle at least, complete nomological explanations for those items that lie within its domain. But most things that require explanation lie outside the competency of science, including axiological explanations, such as why the First World War happened, why rape is wrong, why I think this painting is beautiful and you don’t, and why the economy is in such a mess. Nor will science ever explain why something exists rather than nothing, because its scope is to investigate “somethings” once they exist, be they quantum fluctuations, mathematical relationships, laws of nature, or elementary particles. The ability to provide explanations regarding things that exist is not the same as explaining why anything exists rather than nothing.
There is nothing that science should not try to explain, provided that it seems reasonable to suppose that what needs explaining lies within the domain of science. Unfortunately, not all scientists have made that distinction, leading to a waste of time and public money, in addition bringing embarrassment to the scientific community. Care should also be taken in distinguishing between science and scientism, the idea that the scientific explanation is the only one that counts. In practice, complex systems require explanations at many different levels, only some of which count as scientific explanations. A scientific explanation of the workings of my brain cannot provide, in principle, an exhaustive explanation. The “I” language of personal agency is complementary to the “it” language of the neuroscientist, providing its own explanations for things based on qualia and conscious experience. It is the explanatory, non-science “I” language of our personal biographies that we care most deeply about.