With his speech to the Muslim world at Cairo University on Thursday, Barack Obama put a new face on American foreign policy, or at least a face that the world has not seen since the 1970s. This is America’s penitent, humbled and even sycophantic face. President Obama seeks a “new beginning” to US-Muslim relations through frank self-examination and mutual respect. The US is locked in a battle for the hearts and minds of Muslims, whether it likes it or not. Self-examination can be a sign of strength. But we should not delude ourselves that the Muslim world sees it as...