Why did William and Mary share the throne?

According to "Scotland: A Concise History" by James Halliday, Mary would have succeeded James II, but James had another son in 1688 described as "unexpected and inopportune". So William of Orange (ruler of Holland) was invited by the English to come and bring James into obedience. He did and ran James into exile. After some confusion the English parliament conferred the joint (England and Scotland) crown upon William and Mary. Simply put, William and Mary were married. They were also cousins, William being the son of Charles II's sister, Mary, who married William II of Orange. Thus William also had a claim to the English and Scottish throne (I believe he was right after Mary and Anne). However, William did not want to be king through Mary's grace, but through his own (He did not want to be tied to Mary's strings) and he also wanted to remain king if Mary predeceased him (which she did). These were the conditions of his acceptance of the English and Scottish throne.