An increasing divorce rate tends to increase the inequality of income because it is often the case that one member of the divorced couple comes to be less well-off than before the divorce.
You might think that divorce would not contribute to inequality. The former husband and wife would simply split up and would still make the same amounts of income that they once did. However, this is A) not true and B) might still contribute to inequality when it is true.
When the couple is together, their income is pooled. If one partner makes much more than the other, it does not contribute to inequality because their incomes are counted as one household income. Therefore, a woman making $80,000 and a man making $40,000 are not contributing to inequality when they are married. If they do get divorced, there are now two households, one making twice as much as the other and inequality has increased.
In addition, divorce can detract from the ability of one or both partners to earn. For example, imagine a situation in which a divorced woman has custody of the children. She is now a single parent and has less flexibility in her schedule because she must care for the children. This might reduce her ability to earn. Meanwhile, her ex-husband has as much or more flexibility as he had before the divorce and his ability to earn might well rise.
In these ways, divorce can contribute to inequality.