For a lot of people, geometry is their primary or perhaps only exposure to proofs. Not that everyone needs to understand proofs in their day-to-day lives, but it's a good mental discipline to at least be exposed to, and geometry proofs are fairly straightforward and relate to things that many people will have a good intuition to convince them that the thing proved by each correctly-constructed proof is really true.

Also, geometry gives students something concrete to visualize, and so might be easier for some to understand than more abstract kinds of math.

Maybe trig is over-emphasized at the high school level, but it is pretty useful in a lot of real-world situations, and it's easy to apply without having to know a lot of other stuff.