Their biggest point on the idea that there is no such thing as an immortal soul is two fold: 1 Tim 1:17 in the only place where the word immortal exists in the Bible and it is describing God (there are many other verses that imply it like 'I am Alpha and Omega' and 'I do not change'), and the other point is that the words immortal and soul are not even in the same sentence anywhere in the Bible.