I agree with you. What looks good to university admissions is to be authentic. A big part of being authentic is to do what is right for you.
Also, high school students in the US are under way too much pressure. There are way too many students being treated for stress related problems. Trying to do too much is a common problem.
One thing that you might want to read (and then show your mother) is the “applying sideways” blog on the MIT admissions web site. The point of this blog is that the best way to get into MIT is to do what is right for you, and to do it very well. The same approach works for other top schools.
However, what was right for me, what was right for my wife, what was right for our older daughter, and what was right for my younger daughter, are four entirely different sets of things. Each of us doing what was right for us has worked very well for my family (on a Columbia, MIT, Stanford level).
I think that gymnastics is a great EC. It would be entirely the wrong EC for me, but this is not about what is right for me. It is about what is right for you.