good! that metaphor is a favorite of mine too
you asked about a "center" of expansion
expansion does not require a center
In a rising loaf of raisin bread ANY raisin will do as a
center from which to see the others receding
If the dough is expanding uniformly then you can pick any raisin to take as your point of perspective and it will look the same
from any raisin's perspective. the other raisins (or galaxies) will
all be drifting farther and farther away
and the farther they already are the more rapidly they will be receding.
(one possibility cosmologists have to face is that the universe is infinite, which means picturing that the raisin dough extends, and has always extended, without limit in all directions. but even then it can still be expanding. and an infinite expanding thing has no center away from which it is expanding, no need to talk about this unless professor insists----we do not know for sure if U is finite or infinite so there is some danger of confusion and disagreement about it)
be careful if you try to use the balloon analogy, or if someone tries to use it with you. It LOOKS as if the balloon has a center from which expansion is occurring. But that is actually outside the "universe" which, in that analogy, is just the 2D rubber skin of the balloon. within the rubber skin there is no special point from which you can say the expansion emanates. All points are equally the center of the expansion.
Raisin dough is usually safer because it is 3D, like the space we see around us.