although down the groups (generally) the most loosely held electron faces a lower nuclear attraction, the difference in reactivities (as evidenced by the ionization energy in data booklet) is because in group 2 metals need to lose an electron to react and since the nuclear attraction down the group decreases, it becomes that much more easier to remove an election aka for the metal to be oxidised.

However for group 17 halogens, the atom needs to gain an electron to form a negative ion (aka reduction). Since the valence shell electrons of eg. Flourine face higher nuclear attraction than Chlorine, it is much easier to receive an electron as the atomic radius is smaller compared to Chlorine which has a much bigger atomic radius.