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.