It is clear that mother is utterly wrong feeling guilty in "the cat in the hat", there are stories where gender is unclear and stories where female charaters are the only charaters. Likewise, many of his books are specifically adjusted for both genders, such as "Oh The Places You'll Go"
Dr. Seuss has never been about putting one person above the other. His works are about innocence, the wonder of the world, and being yourself. This growing focus on equality is actually causing inequality in many cases. Dr. Seuss' work should not be about gender, or race, or anything like that. It should be about being a person.
When reading the Dr Seuss books in the modern world, it is striking just how few female characters feature in his work. The vast majority of the characters, both major and minor, are male. In addition to that, females are sometimes spoken about in a dismissive or patronising manner for the sake of jokes in the text.
Writers generally write based on their own experiences, and they create characters that they can relate to. Dr. Seuss grew up in an era where women were second-class citizens. They were not seen as equal to men, so of course his writing would reflect that. He was also a man, so naturally, he can identify more with men, and most of his main characters are men. If women are underrepresented in his work, it is not because Seuss himself is sexist; it's a reflection of the sexist beliefs of the time he lived in.
A look through Dr. Seuss' work shows that there are very few female protagonists. Instead, females are not easy to find in Seuss' work at all. Seuss just presumes that most of the fun characters in his work are men. This doesn't set a good example for young girls that read his work.