Is getting a lot of miles on a car actually bad for the car if the car is well taken care of?

Back story: I have been using my car to visit a guy who lives about an hour away from me, and my mother has said that I "don't need to be putting all those miles" on my car. It is a well-taken care of Ford mustang with about 125,000 miles on it, and I have not noticed any issues at all. Cars are meant to be driven, in my mind.
Is putting mileage on a care actually a bad thing, or is mother probably pulling an overprotective mother of an adult child?

Short trips do just as much, if not more damage than say an hour on the highway.

Stop and go with a cold engine is about the worst thing you can do to an engine.

Have a buddy that put 300,000 highway miles on an old ugly Volvo that he bought for $200. Have other friends that only did short trips and fried their engines before hitting 100,000 miles on a car they blew $20,000 on.

Perhaps both, but it's a real thing. There are but so many strokes of an engine in the average life of an engine (for example). Only so many miles on brakes, water pumps, alternators… "Taking care of the car" will certainly have it 'live' longer, but eventually everything breaks down. People tend to watch the amount of miles on a car and pay less for one with lots of miles.

The actual condition of a car is more important than miles, although when you decide to sell the car or trade it, the buyer or dealer will deduct value, the higher the mileage, because buyers consider high mileage as a negative, even though the car might be in great condition.

We average 15000 miles yrly.
We run most our cars to 275 - 300k miles

Mom isn't concerned about your car.

She's wondering why you're driving an hour away to visit a guy that she hasn't met yet.