Each country - and each demographic of women in that country - has its own history regarding the right to vote. I can only speak to women in early America and while there are a number of factors that contributed, generally speaking, it was because it was felt they had more important things to do. For the purpose of this response, I'm going to focus on white girls and women.

To be sure, the decision to not enfranchise women at the same time as men during the formative years of America as a country was a sexist decision, based in a patriarchal worldview. At the same time, general sentiment among colonists was that white women's responsibility to the new country could be found in the home and the family and they simply didn't need to vote. The concept of "Republican Motherhood" was coined in 1976 by historian Linda Kerber to describe a framework for thinking about the role girls and women were expected to take in early America. The concept itself is difficult to pin down as it's fairly paradoxical: girls and women were expected to be educated enough to be able to discuss politics, economics, etc. with her husband, son, father or other male relatives but not too educated as to seek to shape or dictate policy. However, not all American white girls and women experienced the construct the same. Some, most notably the wives and daughters of the Founders and their contemporaries, found the framework shaped their lives in ways that were progressive and restrictive. Meanwhile, women who were indentured servants or with access to limited means, often found their formal education limited or dramatically restricted.

As an example of how the concept could be both liberating and restrictive, Emma Willard, the daughter of a farmer who subscribed to idea that his daughters were entitled to the same education as his sons, partially because it would help them be good mothers, was an advocate for women's education and instrumental in establishing schools and seminaries. She pushed hard and argued that girls and women deserved an education for its own sake - because they were thinking creatures and deserved to better understand the world. Men, including Thomas Jefferson, told her that women's education should be in service to the boys and men in her life, not to her own needs. This same thinking carried over to voting; There was no need for women to vote because the men in their lives would vote in the best interest of the girls and women in their lives. Willard, it should be noted, had to walk a very tight line. If she pushed to hard for women's involvement in the decision making process outside the home, she'd be seen as unwomanly or otherwise a disgrace to her gender and would lose the attention - and funding - from the men whose support she needed to fulfill her vision for girls and women's education.

From Mere Equals: The Paradox of Educated Women in the Early American Republic by Lucia McMahon:

Republican motherhood elevated women’s status as primary caregivers, giving them a sense of cultural and moral authority. Yet, by insisting on women’s inherent nurturing skills, maternal ideals often silenced the tensions that women experienced while performing the physical and emotional work of mothering. Writing enabled women to give voice to their aspirations, but many women were not comfortable ... seeking publication of their literary efforts. Reform work provided women with an acceptable “sphere of influence,” but the nature of women’s reform remained constrained by a gendered ideology that stressed women’s work on behalf of others rather than the pursuit of individual ambitions. In all these activities, strong articulations of sexual difference increasingly defined women’s experiences and identities.

So, it's not so much the Founders looked at their wives and thought they didn't deserve or shouldn't have the vote. It was more a broadly accepted norm that the work girls and women did was as important as the work men did and there was no need from women to participate in the voting process.