Why can’t I make my friends account my home xbox

You shouldn't have access to your friend's account. That violates the code of conduct and can get you both banned.

Why can't my friend make me his home Xbox when I have him as mine but when he tries it says you can have up to 3 accounts as home Xbox every year?

She can’t use your gold on her friends console unless your account makes her friends console the home console. They can only use your gold on the home console.

Then why make it available to make my home xbox for different accounts

Have you done this before on a different console? You are restricted to doing this only once every 4 months to prevent marketplace theft.