What does the following sentence mean? It's about a veterinarian. "He’s playing reptile midwife."?

A midwife is someone who helps women deliver their babies. So this person is saying he is helping a reptile deliver babies - which is sort of a joke, because reptiles lay eggs I think, but it means to act as the one helping with the mother delivering the babies.

He's helping a reptile lay it's eggs.

A midwife helps women in labor. So I guess its a humorous or degrading comment about a veterinarian, that he helps lizards deliver eggs.

It is misleading because reptiles do not do live birth. I cannot tell if he (the vet) is helping reptiles lay eggs, or helping eggs to hatch.

The basic idea is, of course, that a midwife is a woman who helps a woman when she is giving birth, having a baby. So, midwifing would be to assist in giving birth. But reptiles don't give birth. they lay eggs, and the eggs develop and hatch, and the hatching is usually seen as the birth. The reptiles are almost never around when that happens, and they do not do anything during hatching (even midwifery for their own hatchlings), although some do guard the eggs in the same way that birds usually do.