O1 is an inferior visa, so they are right that you should be trying for H1B before going for an O1. I'm assuming that you are on OPT or some other visa category. There is likely no advantage to getting an O1 in your current situation.
Yeah, if your F1 expires before your OPT, it makes sense to try for an O1. It's a minor expense for the company. Escalate it through your management chain.
