It is said in PCB design, that it doesn't matter how fast the electron moves( i.e current), rather what matters is how fast the electromagnetic field moves.
I'm guessing you are looking at something that is discussing coupling of energy from one trace or wire to another? At higher frequencies, it could be said that the magnetic field changes faster.
Current is the volume of electrons.
How fast the electrons move is "somewhat" constant.
but doesn't how fast the electron moves depends somewhat on voltage.
And also, it was said the flow of magnetic field decides the quality of signal flow, not current... why?
You might not be giving us the whole statement, because that statement is wrong. The current does matter because the magnetic field is produced by current.
Mutual inductance occurs between the close wires in a PCB. Is this from a class? They need to teach you about inductors. There is also capacitance created between wires with would affect high frequency signals, but that doesn't depend on magnetic fields.