Very often what we think about our behavior is not the same as what others think.
You may think you are calm in your talking, but someone listening might say to you - why are you shouting? But you do not think you are shouting. Because we are all different, we perceive differently.
I really cannot judge whether you or your mother is right. But I have a different question for you. That question is - are you very kind to your sister?
My guess is that if you are honest about this, the answer is "no,' I am not very kind to my sister." The reason I guess this is that I would find it hard to believe that your mother says you are mean when you are being extra kind.
You yourself only claim that you are not mean to your sister, not that you are very kind.
So, here is my suggestion to you. Forget about "not being mean." Instead, start thinking about 'being extra kind" to your sister.
I am not sure who of you is the older one, But my guess is that you are the older one. Either way, your being "very kind" will change the atmosphere, bring out the best in you and your sister, and create a bond of closeness that will last for a lifetime.
I am proud of you for asking this question. A lot of times we get caught up in our own lives and it is hard to see the choices we make can hurt others. I do not know how old you are, but try thinking about if you were in your sister's shoes. Would you want her to treat you the way you treat her? Would you want her to talk to you the way you are talking to her?
In the Talmud, there is a story of a very famous rabbi named Hillel. One day someone came to him and asked for Hillel to teach him the entire Torah while standing on one foot. (It sounds kind of funny, but the guy was being mean to Hillel!) Hillel responded: "What you do not like done to you, DO NOT do that to others! This is the entire Torah and the rest is commentary: Go and learn!"
Hillel shows us the golden rule, but by using a negative form, it is even more clear! If you would not want your sister to talk to you the way you talk to her, then your mom is right. Even if your sister is being mean to you, too; you will be happier if you are even nicer to her!
If we look at the stories of Genesis, we see that it is in the nature of siblings to get on each others' nerves, at times. A lesson we can learn though, is that at the end of the day, our siblings should always be there for us. This might take five years or twenty years to see, but one day we realize that all of our childhood fighting and sibling rivalries are silly and that our brothers and sisters are the best friends we can have.
The key phrase of your question is "it doesn't seem that way to me" Maybe it doesn't seem mean to you--but it MIGHT seem mean to your sister. I hope this helps.
Sometimes we think we're doing the right thing, but I find that often we don't know how our actions are understood by others. Look at the story of Joseph, for example. He was trying to be a good son, telling his father when his brothers were misbehaving out in the fields, and liked to share his dreams with his family. Perfectly innocuous, right? Except that the text tells us Joseph's brothers grew to hate him because of his actions and his dreams (enough so that they plotted to kill him, and 'only' sold him into slavery), and even his father Jacob, who loved him best of all, started scolding Joseph and paying more attention to his words.
The next time it comes up, I would ask your mom what she means that you are 'mean'. Explain what you think you're doing, and ask for suggestions for a better way to do the same thing. And then, even if you think you're in the right, apologize. Explain that you're trying to help, not hurt, and that you will try to do things differently, and she needs to let you know when it's appropriate or not.
Family is often hard to get right, but at the end of Genesis, Ephraim and Manassah, Joseph's sons are blessed together by Jacob, and the rabbis remind us that they never fought with one another. We all can't be Ephraim and Manassah, but we don't have to be Joseph and his brothers either.