Why is the impedance in the parallel resonant circuit maximum at resonance?
All paralleled components produce an impedance that is "product" divided by "sum" and, at resonance, the "sum" part becomes zero because X\$_L\$ = -X\$_C\$. This means infinite impedance because "something" divided by "zero" produces infinity.

The impedances are opposite but equal in magnitude at resonance and, because they share the same voltage, the currents will be equal in magnitude but of opposite sign. The inductive current lags the voltage by 90 degrees and the capacitive current leads the voltage by 90 degrees hence, the net current is zero in the steady-state situation.