While it is not a sin for a man to help his wife out around the house from time to time, it absolutely goes against God’s design for a man’s life ambition to be a househusband while he has a wife that goes out and financially supports him.
God created the man, the male, to image him and thereby bring him glory (1 Cor 11:7). In Ephesians 5:29 the Bible says men are called to provide for and protect their wives as Christ provides for and protects his church.
He created the woman for the man to be a suitable companion (Gen 2:18), the bearer and caregiver for his children (1 Tim 5:14) and the keeper of his home (Titus 2:5). He created marriage to be between a man and woman ONLY with the man leading, providing for and protecting the woman (Eph 5:22-33) while the woman submits to the husband serving him as her earthly lord (1 Peter 3:5-6).
Why do certain men desire to be homemakers and care for the children while desiring their wives to be the primary breadwinners? Because of the corruption of sin within them. Some men may even look masculine on the outside while having very feminine natures on the inside. The same goes for women looking feminine on the outside but being very masculine on the inside. But God calls us as men and women to find this corruption of sin. If we are born into a male body, then we have a certain role to play and we are born into a female body then we have another role to play.
It is one thing if a man’s wife becomes disabled and he has to step into her role in the home or the husband becomes disabled and the wife has to step in his role as the breadwinner. That is not what we are talking about here. What we are talking about is when a man and woman plan and choose a life where he will be a househusband and she will be the breadwinner they are planning to break model of Christ and the church which they were both created to model in the institution of marriage which God created.
For a man to seek out the role that God specifically gave to woman is a sin against his creator.