Resulting magnetic flux in the core of a transformer

In a transformer, let's say we have:
$I_1, I_2$ - currents through the primary and secondary winding
$V_1, V_2$ - voltages
$N_1, N_2$ - number of turns
$F_1, F_2$ - magnetic fluxes through core, produced by the currents $I_1$ and $I_2$ (they are opposing...)
$R$ - the reluctance of the core

We have $$\frac{V_1}{V_2} = \frac{N_1}{N_2} = \frac{I_2}{I_1}.\\ F_1=N_1*\frac{I_1}{R}, \hspace{2mm} F_2=N_2*\frac{I_2}{R}$$ I think $I_1$ and $I_2$ are in phase too.
That means $F_1$ and $F_2$ are practically equal.
How can we have a nonzero resulting flux through the core? $F=F_1-F_2$
If the flux through the iron core is zero, then the cause that produces $V_2$ (variation of the flux) does not exist, then $V_2=0$?

Transformer