The universe does expand at more-or-less the same speed in all directions. But because of that, there is no center to the expansion. An observer will perceive themselves to be at the center no matter where they are.
A common analogy is a loaf of raisin bread that is rising. Each raisin in the bread can be thought of as representing a galaxy. For each raisin’s point of you, all of the other raisins are moving away from it with the father ones moving faster.
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