Character Analysis
Milne portrays Kanga as the ultimate mom. We'll start by showing what he means by that, and then throw down some 21st century, equality-of-the-sexes-type perspective.
Mommy Dearest
Kanga is introduced to us in the act of watching over her child, Roo: "Kanga never takes her eye off Baby Roo, except when he's safely buttoned up in her pocket" (Winnie-the-Pooh.7.42). Later, Pooh asks her, "'I don't know if you are interested in Poetry at all?'" 'Hardly at all,' said Kanga" (Winnie-the-Pooh.7.80-81). Granted, Pooh's question comes with the sinister intent of trying to kidnap her Roo, but still, she's immediately characterized as having little to no identity or interests beyond watching her child.
The Age of Equality
Now, identifying as a mother and taking pride in that role is one of the most important things a person can do in this here wide world. Milne gives Kanga some remarkable moments. For instance, she's the only one who really gets Tigger when he arrives in the Forest: "She knew at once that, however big Tigger seemed to be, he wanted as much kindness as Roo" (House.2.129). But a real person also has some interests beyond childcare. A bit of autonomy, if you please.
Instead, what does Kanga do with her time off?
Now it happened that Kanga felt rather motherly that morning, and Wanting to Count Things—like Roo's vests, and how many pieces of soap there were left. (House.4.37)
Of course, in Milne's day this was pretty much the expectation for women in the household, and her stereotyped role is highlighted by the fact that Kanga is the only female character in the book. We're not saying Milne was trying to perpetuate a male-centric culture of childhood, but he certainly doesn't fight against it.
A quick note: it's still less common to find a female protagonist in children's literature—especially illustrated literature—these days. Most heroes and secondary characters are still boys. There are a lot of thoughts about this trend, and it's worth forming your own. A good way to start: would any of the characters in Winnie-the-Pooh fundamentally change if you switched their gender? If yes, how and why?