Biden only has the authority to assert executive privilege, it is pretty clear he does not have the authority to deny executive privilege.
So, what you said is not true.
The reasons should be obvious but are spelled out in this "legal summary"...
"A current President may be all too willing to allow disclosures that may undermine the reputation of a predecessor of the opposing party and may not be fully aware of why certain documents or materials raise legitimate privilege concerns. This is likely why the Supreme Court, in the one case considering a former President's privilege, was not willing to dismiss a former President's claims."
A categorical rule barring former Presidents from asserting the privilege would sweep too broadly, but that is the start, not the end, of the inquiry. Just because the privilege is invoked does not mean it should prevail."
Once a President asserts executive privilege over documents produced during the presidency, the decision about whether those documents are in fact protected by executive privilege become a legal matter for the courts and not something the current serving president can decide.
What is clear the standard for executive privilege protection is higher for a serving president then one who is not currently serving.