Advice from a 20-year-old to the homeschool student:
Dear [Homeschool Student],
Thanks for sharing your heart about school! I know it's tough trying to study and pitch in when the family needs it, too! Oh, well, that's real life :). Those in school/college live in a bubble where they don't get interrupted and don't have to be others-centered, and then they're shocked when they return to the real world after graduation and can't do only what they want any more!
You mentioned how you find it hard to see the point in studying biology, since you don't plan to go on with it in life. I was reading Preparing to Be A Help Meet, by Debi Pearl yesterday, and there was a page in there on how those seemingly useless subjects can really aid you one day as a mother. Just think if you have a son who wants to become a surgeon - the main subject he would need to study would be biology, to be familiar with how a body works. Since you're studying it now, you will be able to discuss it with him one day, and understand a little when he gets so excited to learn some miniscule fact. What you're learning now, even if it's not your thing, will be a platform for your children to stand on to go way beyond you.
Take it to something simpler. What if you didn't know how to read? Wouldn't that put your children at a huge disadvantage for progressing in life, because you didn't value reading, you wouldn't make it be of importance to them. Maybe one of them was destined to become an incredible author, but if you didn't learn how to read, he's at a disadvantage, see? So with biology, the little that you become exposed to can be enough fertilizer for him to explode into his own world of interest!
Also, it's incredibly important just to be aware of the different subjects, even if you don't think you'll remember what you learned in a subject that didn't interest you. Why? Because it helps you to have a peek into understanding what people who give their life to biology do all day.
My mom (Renee Ellison) told me growing up, "It's EXPOSURE that you're getting, exposure." You're getting exposed to a subject, so you know something about it, which is part of being an educated person. Say one day you run into one of the world's top biologists. If you didn't know a little about biology, you wouldn't even be able to say more than hi to him. But if you did happen to study biology when you were 14, then you could have a conversation with him about his newest biological discovery, and you'd be able to be inspired by him.
Also, with the world we live in now, it is critical to study biology because of the ways Satan is starting to use it. At Summit Ministries, they teach about the Brave New World of BioTech which is using technology to mess with the Creator's biology. For instance, I did a web search for "incredible biology breakthrough" out of curiosity, and it brought up such spiritual fighting grounds as turning zygotes into animals, cloning, using stem cells from aborted babies to "help" science, etc. If you didn't have the slightest idea what a zygote is or how a cell reproduces Yahweh's way, how far could you get in a discussion with an atheist who believed engineering a different way of reproduction was perfectly fine!
Dr. David Noebel (who founded Summit Ministries) is such a broad reader that one person caught him reading a book on nuclear physics! Not a book about worldviews or socialism or communism (he reads those at other times), but nuclear physics! That's an incredibly tough subject and he was reading it for exposure! Not that anything in his life ever would require that knowledge (like you mentioned), but for the purpose of being a broader person, and being able to marvel more in worship at Yahweh's awesome acts, and to keep growing his brain and putting new neuro-pathways down on topics that he had never thought of before!
As dominion-takers in this world, we have been given the commission of working our mental soil, and constantly growing the seed in it, in order to be better ambassadors in this world. Our call is to be ambassadors that the world respects because of our skills and knowledge, and not ones that the world despises and thinks not worth the time to listen to, because we don't know how to spell or what the dorsal side of a frog is :). If we know what we are talking about in common subjects that they have studied too, they will be more likely to listen when we talk about spiritual matters, which they may not have looked into so much. We gain their respect because they agree with us on the common intellectual ground.
I asked these questions too, and needed someone to widen my vision, so I'm so glad you asked so I could share what I have come to know!