I didn't see where he said that, but the was politicians twist words, he could be referring to the fact that in theory anyone with a draft status, even 4-F, could have been called up in a "national emergency"
There used to be a classification, I-Y, for people with less serious medical conditions, who would be called up in a declared war but weren’t being drafted during the Vietnam War. About 1972 it was abolished and those with that status were reclassified.
Biden didn’t explain his rejection from the military I found the information on google.com