What causes someone to have bipolar I with rapid cycling?

Genetics & triggers. Rapid cycling bipolar d/o involves 4 or more discrete affective episodes in a year. It is more frequent in women, associated with hypomania, hypothyroidism, stronger family hx, & higher exposure to antidepressants (though it may be depression itself that leads to both rapid cycling & increased antidepressant use). Careful evaluation & management by a skilled psychiatrist is essential.
Combined factors. The best we can tell, it's a combination of genetic vulnerability and ongoing biopsychosocial modulation. People may have individual triggers for episodes, and discovering & dealing with those is part of the work one does with one's own doctors.