What is higher reasoning?

It's akin to reaching a higher moral ground. Similar to the following examples.

A surgeon has higher medical reasoning than a regular MD, than a paramedic, than a First Aid trained person.

Physics is defined by certain rules that somehow don't apply to quantum physics giving the latter a form of higher reasoning.

Morally, it's reaching a level where your morals follow the greater good instead of personal advancement.

It's a catch phrase made to define yourself as better than others.

Commonly used by arrogant people.

After having worked with homeless people, I know now that you can be street smart in a way that defeats reason, and you can be so educated as to lose all usefulness to people.

This explains why people sometimes disagree with God.

We simply haven't got the tools to see things His way.