Why can the coronavirus tests say that you do not have it … but it turns out that it is yes as it has happened to Carmen Calvo?

For starters, yes it's true, Vice President of the Government Carmen Calvo his two coronavirus tests have given him opposite, but not contradictory results (despite having symptoms of having it). Although in the first of the tests the result was negative, the verdict also included the "inconclusive" tag, and it is in that tag where the key is (and the reason why the test was repeated days later).
The test that has been done in duplicate to the vice president is the most reliable at the moment to detect the coronavirus: the PCR test. What this test attempts is to detect in the sample that genetic fragments of the pathogen being investigated (in this case the coronavirus) are extracted from the patient. If there are traces of your RNA (in fact, several different markers are searched to make sure) the result of the test is clearly positive and the patient goes on to swell the list of those infected, but if those fragments of RNA that are sought are not found, it is negative.
But sometimes the results are not clear, only one of the three or four markers is found and that is what has happened to Carmen Calvo who gave a “negative inconclusive” result. In this case, the test is repeated days later to confirm whether you are dealing with a new patient infected with coronavirus or not.
This indeterminacy in the result may also be due to other factors, such as the sample was not drawn correctly (it has to be removed from the nasopharynx through the nose, and yes, it is as annoying as it seems) or the patient is at the beginning or at the end of the process coronavirus infection that there is not enough viral load so that the result is clear.
How PCR tests are difficult to do and their results are slow (they take hours to confirm a case) in China, at the top of the spike in infections, another system was chosen to recognize the positives: they assumed that the majority of their population was possibly already infected, people were classified by symptoms and the most suspicious had a CT scan (computed tomography) that takes images of the lungs of the patients: apparently the traces that the coronavirus causes in these organs are identifiable to the experts at a glance.