Instead of “The reason is because I thought it was mine,” one can write, “The reason is that I thought it was mine,” “The reason is, I thought it was mine,” “I took it because I thought it was mine,” or, simply, “I thought it was mine.” (“Because I thought it was mine” is acceptable in informal usage.) In place of “I want to know the reason why you took my book,” one can write “I want to know the reason (that) you took my book,” “I want to know why you took my book,” or “I want to know your reason for taking my book.” Yes, “the reason why” and “the reason is because” are redundant - guilty as charged. “The reason is because” has no supporters, but “the reason why,” despite also being idiomatic, is ubiquitous even among highly respected writers.
But that stance (or, at least, part of it) is shaky. Many well-meaning writers and editors condemn “the reason why” and “the reason is because” for the crime of redundancy. Is There a Reason “the Reason Why” Is Considered Wrong? By Mark Nichol