Is it unreasonable for the company not to tell me the number of outstanding shares?
Yes. Your logic is absolutely correct -- they're refusing to tell you something which is essential to you being able to evaluate their offer. You (hopefully) wouldn't accept a job offer without being told what the salary / hourly wage is; you should treat this situation no differently.
I told them I was going to take the night to think it over. I guess tomorrow I will ask again for the number of outstanding or authorized shares. I feel like if they continue to be sketchy about it, it might be an indicator of how they will act in the future.
Yes. Your logic is absolutely correct -- they're refusing to tell you something which is essential to you being able to evaluate their offer. You (hopefully) wouldn't accept a job offer without being told what the salary / hourly wage is; you should treat this situation no differently.