I find Conrad's cartoons amusing, but if he is going to include Catholic doctrine in his drawings, he should quote the correct doctrine.
The Immaculate Conception means that Mary from the moment of her conception was free of original sin. Mary, however, was conceived by her parents through sexual intercourse, just as every other human being.
Christ, however, was conceived by Mary without sexual intercourse through the power of the Holy Spirit. This doctrine is known as the Virgin Birth.