There is a difference between a person having STANDING to bring a defense based on a privilege in court and the defense actually being accepted.
In this instance, former presidents have the RIGHT to invoke executive privilege over communications they engaged in as president. But it is up to the court to determine whether the particular communication at issue falls within the privilege's protection.
Trump, as a former president, has the standing to assert executive privilege in this case. But the communications at issue are unlikely to qualify as privileged, given a variety of factors, including the fact that they involve criminal activity unrelated to the duties of a president and they were engaged in with people who were not on his staff at the time of the communications. He also has to show that the communications are so sensitive and important that revelation of them can negatively impact the country - that's where Biden comes in. By refraining from joining Trump in the invocation of the privilege, he's essentially saying that disclosing that communication won't cause any damage and that's going to be given considerable weight since he's the person currently responsible for the well-being of the country.
I hope that makes sense - it's both complicated and also very simple and logical.