Unless the meat is pastured ruminant, your mom is more right than wrong.
"I'm too busy" means "I'm prioritizing something else above my nutrition". Maybe this is legitimate. Maybe every spare second of every day is truly being used productively on things that are more important than your nutrition (or, at the very least, unavoidable). More commonly, people who say "I'm too busy" manage to make time for TV, video games, messing around on the internet, reading for pleasure, exercising beyond their actual physical need, or any number of other things that are not actually more important. (Also, is your mom busy? Does she work outside the house? Does she do other household chores? Does she ever spend time cooking when she'd rather be doing something else?)
While rebelling against parents fulfills a psychological goal in encouraging independence... everyone involved will probably be happier if you find discreet ways of adding saturated fat rather than making a big deal about slathering butter all over the meat that she carefully trimmed. Throw some coconut oil or good quality butter in your broth, coffee, smoothie, or whatever. Eat an avocado. Make a good salad dressing with appropriate oils.
Learn to cook. This is SO IMPORTANT. At some point in your life, you're probably going to be cooking for yourself, and it's probably going to be harder to learn later. A lot of people don't hit the "I have to cook for myself" point until they're trying to juggle college and a full-time job, or have a kid and no excess money for preprepared food, or until they're divorced at 50. And often these people end up falling back on bad choices because they don't think they have the time or energy for better. Learning now when you have the safety net of your mom's cooking is one of the best things you can do for your long term health.
Frying up some eggs or a thin slice of meat takes just a few minutes. For more complicated stuff, look at once a week/once a month cooking techniques. This is really easy if you're just cooking for yourself - spending a few hours (tops - it can take much less time) preparing a meal or two designed for a whole family will take care of the majority of your food for a week. Throwing stuff in a crock pot is quick and easy, as are most roast meat/veggie recipes. Seriously - my 8 year old can handle them.