I am puzzled of the “Andromeda–Milky Way collision”, when everything is moving away from the center of the Big Bang?
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There is no “center” of the big bang. Everything is moving away from everything else in all directions.
However, the rate to which space stretches is very, very small. Your body isn’t being torn apart by the expansion of space nor are you being thrown off the Earth’s surface.
The other forces acting on you (the electromagnetic forces holding your molecules together, gravity holding you to the Earth) outweigh the effect of the expansion of space by many orders of magnitude. Local forces dominate the situation.
It’s the same on the scale of galaxies. The milky way and andromeda are much farther apart than you and the Earth, which does mean the expansion of all the space between them is a bigger deal. However, they’re also extremely massive. They’re still close enough that gravity “wins” and the galaxies get pulled together. Other, more distant galaxies are more weakly bound, gravitationally, to the milky way and have even more space between them and us. In these situations the expansion of space beats out gravity and those galaxies move away from us.
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