In France, how did the Declaration of the Rights of Man and the Declaration of the Rights of Woman exemplify the gender divide between those who supported revolutionary change?

The Declaration of the Rights of Man and Citizen was by no stretch of the imagination a feminist document. It was devised by men for the benefit of men. Despite its emancipatory rhetoric, the Declaration made no mention of support for women's rights. And this omission was by no means unintentional. The men of the French Revolution didn't regard women as being equal, and so didn't believe that there was any space for them in the political realm. Women were held not to be citizens, and as such were systematically excluded from public life. The role of women in the new society was to be pretty much the same as under the ancien regime.
It was in response to the blatant deficiencies of the Declaration that the radical revolutionary and feminist Olympe de Gouges drew up her own proposal, the Declaration of the Rights of Woman and of the Female Citizen. This Declaration was incredibly radical for the time, not least because de Gouges argued that women were entitled to equal civil and political rights on the basis of natural equality with men. Revolutionary opponents of de Gouges attacked her on the grounds that the whole notion of women's rights was contrary to nature. Women, they believed, were neither physically nor psychologically capable of participating in political life. De Gouges counters this assertion in the Declaration by accusing men of confusing nature with the artificial distinctions imposed by society.