Bury your Wife.
You asked about Toucans not Hornbills. But the birds are similar in habitat and appearance. The Hornbill is the African version of the South/Central American Toucan.
Here is an interesting fact about Hornbill gender roles. They nest and lay their eggs in tree hollows. To prevent predators, some species enclose the female inside with her eggs. They leave only an opening large enough to pass several hundred figs per day, and the male gathers food for his wife and children until they are large enough to fend for themselves.
For Hornbill people this suggests a society where children and mothers are never to be seen in public. Once you have children you are not allowed to leave the house. All contact with the outside world must be done through your husband.
During the last century however the younger generation decided this practice is a massive Hornbillperson-rights violation. It was made illegal and is quickly passing out of fashion.
Mostly in rural parts of the world, some mothers still enclose themselves voluntarily. It is prickly issue whether these women are doing enclosure voluntarily, or whether they are being coerced.
For the most part mothers are allowed to leave the house, provided they do not take their children with them, or act in any way that reveals them self as a mother.
Another type of birds where the males and females are hugely different is peafowl. The males have huge ridiculous tails and the females are much more sensible. The females find these huge tails hot as hell  but they make flying difficult and cost a lot of energy to maintain.
For Peafowl people this might leads to a situation where males are seen primarily as sex objects and the women are the breadwinners. Most buildings are only accessible to women and the men cannot even fit inside without damaging their magnificent tails! Can you imagine the shame of it!
The dream of every peafowl CEO is to build a marvelous golden atrium onto the side of her house where she provides for the every need of her harem of magnificent-tailed husbands, who swagger and shake back and forth all day long and wait for the mistress to come home.