Because, for example, if theta X chooses to make XO very, very likely, then most of the instances where X is unobserved will be assigned to the XO case, and that's going to basically, have me, you can assign the data instances to the x0 and that's going to change the estimates of theta y given x0 relative to theta y given x1 because most of the instances now correspond to x0 rather than x1. 