I haven't read the series, but apparently his mother was a witch.

https://en.wikipedia.org/wiki/Order_of_the_Phoenix_(fictional_organisation)#Lily_Potter

Lily J. Potter (née Evans) is the mother of Harry Potter. She is described as being very pretty, with startlingly green almond-shaped eyes and thick, long, dark auburn hair.

Although Lily is Muggle-born, she is an extremely gifted witch at the top of her class.

https://en.wikipedia.org/wiki/Sexuality_in_Christian_demonology

Heinrich Kramer and Jacob Sprenger (15th century), authors of the Malleus Maleficarum, adopted an intermediate position. According to their book, demons did not feel love for witches. This is because sexual relationships with them were a part of the diabolical pact these men and women made with Satan.

William of Auvergne conceived the idea that demons felt a particular and morbid attraction to long and beautiful female hair, and thus women had to follow the Christian use of covering it to avoid exciting desire in them. Tauler had the opinion that demons were lascivious and thus they wanted to have sexual intercourse with humans to satisfy their lewdness. Sinistrari supported the idea that demons felt sexual desire, but satisfaction and pleasure were not the only motivation to have sexual relationships with humans, another reason being that of impregnating women.

It does all seem to check out. The long hair, the witchery, the demon impregnation, Harry Potter, July 31.