I hate the way my mom drinks tea
What bothers you most about the way that your mother drinks tea?
Because I like to take my tea without any sugar in it
Everyone is an individual with different tastes than you and that's okay. It's important to allow your mom the freedom to drink tea the way she wants to, just as she allows you to drink yours the way you do.
I'm going to throw out all of her tea.
It's not okay to judge your mother based on her preference when it comes to drinking tea. You would want her to respect your preference so you should show her the same respect.