The tension that you describe between you and your mother is common for fatherless daughters. Their mothers often react defensively when questioned about their former lovers. They feel shame and guilt for the pain that they’ve created and don’t want to be confronted with it. Therefore, they push it away. In doing so, they make a wedge between them and their daughters.
It takes an incredibly secure mother to admit her failings. It’s rare for a woman to apologize for being irresponsible and making a baby before constructing a proper nest. She may not want to confess that she conceived a child in a one-night stand or with a married man, a drug addict, an alcoholic, a criminal, or a bum. She may worry that her daughter will lose respect for her or follow in her footsteps. She doesn’t want to be forced to examine the mistakes that she’s made.
With that being said, you should appreciate how hard this is for your mom. If you accept that she’ll probably never open up about your biological dad, you’ll find peace. While it’s understandable that you want to discuss your feelings about him, you must realize that she’s not willing to do that. Therefore, you need to speak with friends, your grandparents, a teacher, or a counselor.
There’s a good chance that your mom knows very little about your sperm donor. Conversely, she may know things about him that she believes would be detrimental to your well-being. If that’s the case, you should trust that she has your best interest at heart.
When you’re older, wiser, and settled in life with a solid education and a good career, you can do a search for your father if you’re still curious. At this time, though, it’s not a good idea to get distracted from your goals. This is the time to honor the people who’ve been there for you, sacrificed for you, and loved you--people such as your mom.