Why can't Vampires enter a house without an invitation?

because there is believed to be a "Spiritual" or "Personal Power" oriented natural magic(occurs spontaneously) that protects what is within the threshold, it is a life sustaining force and the dead or evil are antagonistic to it.

And the Vampire cannot cross a Threshold of a home. the people living there and the natural magic act as a circuit to make a force field-kind of, if the residence is abandoned or very rarely used the "Threshold" is not very strong, same with public places if the intimate personal connection is not there, then the non living or preternatural are not repulsed. this often applies to magic practitioners of various types as well(not illusionists or slight of hand artists)