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.