Upvote:3
I'm going to guess here (no way to know for sure without talking to him), that the term used was indeed a holdover from the days when Blue Discharges existed.
After Congress got rid of those discharges, they didn't stop discharging soldiers for those reasons. They just created two new discharges; "General" and "Undesirable". General was still considered honorable (and thus eligible for some veterans benefits), while "Undesirable" was not. I believe these are roughly equivalent to today's "General" and "Other Than Honorable".
"Undesirable" does seem to have been used for h*m*sexuals (who hadn't engaged in such acts. Doing that got you a fully Dishonorable discharage instead.) until the policy was changed in the 80's. However, it was (and OTO still is) also used to discharge soldiers with mental health issues (eg: PTSD). The military is just starting to grapple with changing this policy, at least in circumstances where a psychological injury may have occurred in the line of duty.
Of course those discharges aren't limited to those causes. A person can also receive them for things like disobeying orders, adultery, fighting, drug use, or anything else your superiors don't like, but don't want to bother with convening a full courts-martial for.