Your husband is a bit misinformed. Having a gynecological exam helps to protect you as a woman against one of the biggest killer amongst women and that’s cervical cancer. That alone as a husband should make him want to support your efforts.
Not to mention as women we can develop all other kinds of issues with our female organs such as cysts or polyps. Taking care of ourselves is vital in making sure that we catch things in the early days. The other flip is that we need to be on top of our sexual health. When I was pregnant with my daughter the doctor asked me since I was married did I want the full exam. I said yes. Now that didn’t mean that my husband wasn’t faithful but let’s be real I wasn’t willing to flip a dice that he wasn’t.
Your husband should still be getting fully tested as well. Knowing your status doesn’t stop at marriage at all. If you’re sexually active you need to know. A ring or a piece of paper isnt going to stop your body from receiving anything. Educate your husband and hopefully when you’re husnand comes out of his feelings he will be mature enough to know this is necessary to ensure your health. An exam can be life or death and he needs to support you in your continued quest for total health.