We celebrate the May date because May is a good time for a holiday (not close to other major holidays, good weather in our part of the world) and December is very close to the date of Solstice and also close to Christmas, Thanksgiving, etc.
8 of may is already taken by a pretty big victory celebration at least in the Western world. 8 of december sounds better
That's a feature not a bug with the 8th of May. The fact that it's already a free day in countries for the purpose of celebrating WWII victory makes it easier to have regular celebrations on that day for other purposes.
Mother's day is likely a bigger issue.
Quite by accident I was at the Jenner house museum (Berkeley, England - worth a visit if you’re in the area) that day and they had a note celebrating the anniversary, but I think they celebrate all year around.
Several of my friends posted on Facebook/threw parties this weekend for a date of May 8. However, searching on Facebook, I find that I and several other friends have been posting celebratory messages on Facebook on December 9 in previous years.
This inconsistency is probably because there are two obvious candidate dates for eradication:
The global eradication of smallpox was certified, based on intense verification activities, by a commission of eminent scientists on 9 December 1979 and subsequently endorsed by the World Health Assembly on 8 May 1980.
"500 Million, But Not a Single One More", which is widely shared and has been adapted at least once for reading at a large Secular Solstice, uses the December 9 date.
I think creating more consensus on which date is the "official" one for celebration purposes would be a small improvement (at the very least: I would stop confusing my relatives by year-to-year inconsistency on when I message them a little commemoration). So, which is it?