In since cases courses designed to benefit your Olympian where possible.

Familiarity as in being able to train on the actual courses, court, apparatus etc. where the event will be held (assuming you train in your home country).

Also in some cases I think the host country influences these things in a way that maybe slightly benefit their own Olympian. Some things are standardized and it doesn’t matter but things like mountain biking courses, cross country ski courses, marathon routes, downhill ski etc. could be designed to benefit the host country athletes. For instance if your mountain biker is good at climbing hills maybe that is an emphasis in the course design.