I presume that the photons from the CMB approaches the earth from all directions, otherwise we couldn't detect them with a picture where it is present everywhere in the universe with a tiny anisopotry.

Now the CMB is a result of the big bang. What also is a result of the big bang is that in all directions we see galaxy move away from us, like we are in the center of the universe (which is probably not the case).

But why are all the galaxies (except a few) moving away from us while the CMB is also approching us. What is the reason for that difference? Or aren't those photons coming from everywhere?