First of all, I think that we should note that the United States was not particularly tardy in giving women the right to vote. This question uses the phrase “took so long,” which implies that the US took much longer than other countries to allow for women’s suffrage. I would argue that this is not appropriate. There were very few countries in the world that gave women the right to vote before 1915. The US was very much in the main wave of countries that gave women this right. So we should not think that the US was especially late (compared to, for example, France, which only allowed women to vote after WWII) in allowing women to vote.
But the underlying question still applies: why did the US wait as long as it did to allow women to vote. There are two main reasons for this. The first reason has to do with the original attitudes about who should be able to vote. In the early US, the idea was that only people who were independent should be able to vote. Anyone who depended on another could be told by that other person how to vote. This made it improper for such people to be given the vote. This was, for example, why only people with a certain amount of money or property were typically allowed to vote in early America. This attitude made it less likely that women would be allowed to vote because people felt that women were always dependent. They were economically dependent on men over the course of their entire lives because society essentially did not allow them to be independent. Because they were dependent, they could not vote.
A second reason has to do with general attitudes towards the competence of women. Women were long believed to be inferior to men. People believed that women were not intelligent enough and did not have the emotional stability needed for public life. They did not think that women could calmly and logically think through complex political issues. Therefore, the idea was that women, like children, could not possibly vote responsibly.
For these two main reasons, Americans did not allow women to vote for a long time after almost all men were officially given that right.