Gosh, I'm not sure of the customs and norms in India. I know that I do and did all of my gynecological care with out my husband in the room here in the states. The doctor normally has a nurse that comes in and joins and if they are examining you. Once I was pregnant, my husband went to some appointments and I've had friends whose husband went to many or all of their pregnancy appointments. I wouldn't say it is necessarily common for a husband to be there during a regular appointment in which a pap smear is done but wouldn't think a doctor would object either. And this was a PRE pregnancy consultation. He want to be in on the conversation about the undertaking of trying to get pregnant. Although ob/gyn's consider themselves the doctor for the woman and not the man during the pregnancy process. A fertility specialist would give more care to the man and his contribution. :>)) Do you have a right to have him? I would say that it shouldn't be such a big deal if he stays but this is your doctor's preference. So, maybe it isn't the right doctor. And I don't know if there is a shortage of good ob/gyn's in your area giving them the ability to dismiss patient requests like this. Can you check on other doctors and you can ask the front desk people if husbands are able to stay in the room during exams. OB/gyn's are generally very busy and they will not sit and talk and talk in a relaxed way the way a general practitioner will. That's pretty common in general, I believe. But if you don't like the doctor and her policies, I'm sure there are others to try to find a better fit with.
My wife and I go to all of our appointments together. I find it very unusual for a physician or other provider to be concerned about your husband being present. If a medical provider is uncomfortable with a spouse being present, unless for a very good reason, like infection risk, I personally would refuse the exam and find a different physician or other provider.