How is it possible that someone can 'un-develop' an allergy?

It is quite common for children to outgrow allergies as their histamine reaction matures.

Susie is right, but actually, science doesn't fully understand how the immune system works in that regard. Childhood allergies often just fade away, but OTOH adults can develop brand new allergies quite suddenly.

As one ages,  your body chemistry changes,  as do sometimes your allergies.