Mrs. Winterbottom fears that revealing Mike is her son is going to damage her reputation in her husband’s eyes. Admitting that she had Mike and gave him up for adoption is likely an admission that she had a baby out of wedlock, possibly as a very young woman—things that she doesn’t expect her upstanding, stoic husband to approve of. With this, Mrs. Winterbottom essentially reveals that she’s been trying to embody the perfect housewife for so many years to try and make up for her perceived fall from grace years ago—but she can’t continue this façade anymore.