Typically, a geometry class in high school teaches Euclidean geometry. Depending on how much time is spent and the exact class, Euclidean geometry as rendered today explores properties of triangle, parallelogram, and circle, while following an axiomatic system, much of which was initially laid out thousands of years ago. The purpose is less to understand these objects deeply per se but to learn how a large set of conclusions can be derived from a few simple assumptions.
In higher education past high school, modern mathematics are taught instead -- either to prepare students to research in mathematics, or to prepare students for applications of mathematics. Euclidean geometry would be rather remote from either. No current research fields draw much from the old school Euclidean geometry -- we are thousands of years past that after all. No common applications require Euclidean geometry either.
In the case of training students on logical rigor, an advanced degree have many more such opportunities. Thus no need to spend time on Euclidean geometry. For high school, some of the more intricate machineries in modern mathematics can be too abstract. Euclidean geometry thus became the quick and more viable way to expose students to an axiomatic approach.
The competition for time should be a thing in high school too. So it's worth mentioning that, in Asian countries, Euclidean geometries are taught in junior high schools. ie. grade 7-9 (though there is little teaching in grade 9 with it being mostly exam prep) where grade 1-6 is the primary school. With that arrangement, any hypothesized benefits would be gained without taking away valuable time in high school that can be used for further education in math -- to teach foundation for calculus (including some basic analysis), probability, etc, which in turn can be especially helpful in preparing students who will enter fields that require applications of math yet won't have a lot of time to spare for math such as the various engineering fields.