Flux in transformers
You could begin an argument about transformers like this: -


A transformer has magnetizing flux due to current flowing into the whole of the primary winding when the secondary is open circuit i.e. the transformer is an inductor.
When extra current flows in the primary due to loading of the secondary this flux increases
The current flowing in the secondary winding also increases flux (incorrect, it totally cancels the ampere turns in the primary due to loads on the secondary)


However, the massive flux generated by the primary due to loading the secondary is totally cancelled by the reverse magnetic flux due to current flowing in the secondary. Consider these scenarios: -




Scenario 1 is just the primary winding with Imag flowing
Scenario 2 is two windings wound close together - Imag (the same as above) is shared by the two windings
Scenario 3 is the 2nd winding open circuit - it has the same voltage as the primary winding
Scenario 4 is the secondary load - Iload currents are in opposite directions and their fluxes cancel.