>>17867855>everything I'm about to say is in the context of the core franchise games, with no derivative works taken into accountIF YOU OBJECT TO MEW (AND/OR LEGENDARIES) BREEDING...
I am hard-pressed to think of a Pokemon that has been explicitly portrayed as a singular, immortal creature. Like any other living creature, they have to reproduce (or otherwise be created) for their lines to live on.
Mew and most other legendaries do no breed in the daycare. That doesn't mean they are incapable of breeding. Their Egg group is Undiscovered, which can be interpreted as "no eggs of this species have ever been discovered." Perhaps their breeding rituals/conditions do not adapt well to a Daycare environment, or are otherwise too nuanced and/or misunderstood by the common trainer to replicate.
IF YOU OBJECT TO MEW "GIVING BIRTH" AS OPPOSED TO HATCHING AN EGG...
a. For all we know, Pokemon which do not produce eggs may be capable of giving live birth. Or, some or all Pokemon are capable of both giving live birth as well as producing eggs. The process of conception may differ between the two. It's always been said that no one has witnessed Pokemon "breeding" to produce an egg, they just appear. Perhaps sexual reproduction is separate from egg reproduction in a way we don't understand.
b. An NPC in Kalos mentions that "eggs" aren't eggs in a literal sense, but more akin to a cradle. Perhaps Pokemon are born via live birth, but are born within a "cradle" (an amniotic sac) that is eventually cast off. Thus, Mew gives birth to an "egg" that eventually "hatches."
c. Given the unorthodox experimentation and manipulation conducted in the Mewtwo project, it's not hard to imagine that the way in which Mew gives birth is also altered.
d. It's also possible that "gave birth" is just a colloquial way of saying "reproduced." If we squash a spider and say "I killed a bug," that is incorrect in a technical sense, but colloquially we all know what is meant.