Mary must be immaculate to conceive Jesus
and that premise is false then the conclusion is invalid.
You’d have to prove that premise first.
“Mary must be immaculate to conceive Jesus” is a whole nuther syllogism, not necessary in the one in discussion. For example, the EO accept the logic of this syllogism, but consider the Immaculate Conception false or not proven.
Here’s the basic theological point: Jesus has two natures inseparably united in one person, that person is one of three Persons in One Godhead. That person is God, the Son in the Holy Trinity.
Mary gave birth, according to Incarnation Theology (and common sense), to a person, not a nature. A person whose two nature cannot and must not be separated in order for the Incarnation and the Holy Trinity to be true.
Any attempt to claim Mary gave birth to a nature or to separate whom Mary gave birth to into two natures is heresy.
I believe this is the theology for orthodox Christians, Trinitarian Christians, and others particularly those saying the Nicene Creed.
One can vary from this theology of course, but they do so at risk of heresy in the eyes of most Christians whose theologians hold the orthodox doctrine of the Trinity and the Incarnation.