I don't have to. You have never seen an electron, yet you can measure and deduce its properties. The probability amplitude peaks at a definite point in space and becomes zero everywhere else only
after a measurement is done. This has been experimentally verified and implemented in a number of applications.
There is clearly the contradiction that LostConjugate spoke about - it's a problem of classical realism and lots of human baggage. But to say that there is no contradiction with our everyday concepts when an electron interferes with itself, is an exaggeration.
Thinking of an electron in motion towards the detector plate as an "infinite pattern" and then interfering with itself gives everyone a headache. If you think you understand how a single electron can pass through both slits at the same time, that's a solid indication that you don't understand it.