Mammogram or no mammogram

So I will be 27 in September and the doctor who delivered my daughter this February wants to give me a mammogram but my original obgyn (he delivered me as a baby and has seen me since age 17, but is retiring soon so he doesn’t do deliveries anymore) says he doesn’t think it’s necessary.

Just a background, on my maternal side, 2 of my grandmothers sisters and my moms 1st cousin had breast cancer and on my paternal side 1 of my grandmothers sisters had breast cancer 2 times. So far my generation has no diagnosis but no one under 40 has had a mammogram yet either.

Is it necessary at 27 or should I wait until the normal age?