Caller ID is a carrier function, and the switch to control it is actually enabled by your carrier. If you don’t see the switch your carrier may not support controlling it from your phone. You would have to call your carrier and ask them to disable caller ID for your number.
Another possibility is if you have a company phone or your phone has a company email account then the IT administrator can disable controlling Caller ID.
Not directly related to your question, but if you call a toll-free number you cannot disable caller ID; the number is toll-free to you, but not to the business you are calling, so they legally can know the caller they are paying for.