Gender does not determine what I can or cannot do

I am a 16 year old girl. I go to high school and have one younger brother and one younger sister. One day, my mother and I were talking about how she will no longer be able to come pick me up from school and I told her that it will be okay, you know, the┬áspring snow is gone so nothing to worry about. I thought she would be on board but instead got mad that I had suggested that and told me that I could not possibly walk from the school to my house (It’s only a 20 minute walk). When I asked her why I couldn’t walk, while our neighbor’s kid who is two years younger than me and is a boy can, she simply told me that he can because he is a boy. My younger siblings heard all that. I do not want them to grow up with the mentality that being a girl means not being able to do certain things such as being successful or walking alone after school. I did talk to my mom afterwards telling her that it was a sexist thought and has nothing to do with what we’re talking about but she didn’t even consider listening to me. I hope things change in the future and people of all ages and sex will finally understand that gender does not determinate what you can or can’t do .