'Skins' or 'hides' signify external things, because the hide is the outermost organ of an animal where its interiors extend, the same as with a person's dermis or skin. 'Skin' corresponds to truth or to falsity in the extremes. See Arcana Coelestia 1835, 10036, and Apocalypse Explained 386. 'Skin,' as in Job 19:26, means the natural degree a person has with him after death.

In Exodus 22:27, this signifies things that are relatively external. (Arcana Coelestia 9215)

In Exodus 34:29, this signifies the internal of the Word shining from the external. (Arcana Coelestia 10691)

In Job 19:20, this signifies being not entirely in falsities. (Apocalypse Explained 556[11])

In Jeremiah 13:23, this signifies that evil cannot change its nature. (Apocalypse Explained 780[5])

In Genesis 3:21, this signifies that the Lord instructed them in spiritual and natural good. (Arcana Coelestia 292)

In Genesis 27:16, this signifies the external truths of domestic good. (Arcana Coelestia 3540)

10036. 'And its skin' means falsity on lowest levels. This is clear from the meaning of 'skin' as truth on lowest levels, and in the contrary sense as falsity there. The origin of this meaning of 'skin' lies in correspondence; for those who in the Grand Man or heaven who correlate with the skin are people who are governed by the truths of faith and not so much by the good which goes with those truths, and who live on the borders of heaven, see 5552-5559. So it is that 'skin' means in the abstract sense truth on lowest levels, 3540, 8980. But here falsity on those levels is meant by it, because 'flesh' means the evil of [self] love, dealt with immediately above in 10035. When 'flesh' means the evil of [self] love its 'skin' means the falsity of faith arising from it.