Think of it like this:
Image a cross-section of the part of a coil passing through an opening in a magnetic core - eg. where it goes though the centre of a toroid transformer or whatever.
The magnetic field originates in the coil and form a circular pattern around it. Think of "lines of force" patterns.
As the current starts and increases, those lines of force - the magnetic energy that is being built up - must spread from the coil and in to the core.
That cannot happen without the energy / field line also passing through any other conductors in that same core opening.
Likewise as the current in the primary reduces, the it's field weakens and shrinks back towards the coil wires.