The horizontal component increases
whenever the angle is decreased.
Imagine being over the north magnetic
pole with a freely suspended magnetic needle.
It would in theory point straight
down at 90 degrees from the local horizontal.
The resultant horizontal component
would be zero.
When at the magnetic equator there is
no inclination, and so there is a maximum horizontal component.
The vertical component will thus be
in the opposite sense.
It is a maximum at the north magnetic
pole and zero on the magnetic equator.