I think my brother should help pay for the costs of a ticket when I borrowed his car with expired registration and no insurance
Why do you think he should help?
Because it's his fault that stuff was expired and uninsured!
I totally understand why you're upset about this!  Your brother should not have let you borrow that vehicle without that paperwork.  The vehicle might've been unsafe to even drive!
I'm going to take this to a him and make a big deal about it.
Definitely it was his fault to lend you a car with expired registration and uninsured. You're right in asking for money to pay for the ticket.