In China the number four is considered unlucky, presumably because the Chinese word for four is very similar to the word for death. This association with bad luck seems to have followed the number four into the wizarding world.
Four is sometimes seen as a source of stability and strength, as in the four sturdy legs of a table. But if one of those legs is weak, the whole structure is in danger. We see this mirrored in the four
lexicon.org/thing/the-sorting-ceremony/">houses of Hogwarts, a system that should provide strength. But with the breaking away of
lexicon.org/character/salazar-slytherin/">Salazar Slytherin, the house system becomes a source of disunity and conflict.
Unlike our main trio, there are four
lexicon.org/thing/the-marauders/">Marauders, and that doesn’t end well for any of them, with
lexicon.org/character/peter-pettigrew/">Pettigrew being their weak link. Pettigrew betrays James, who is murdered by Voldemort; Sirius is
lexicon.org/event/sirius-black-is-killed-by-bellatrix/">murdered by Bellatrix; Pettigrew literally dies by his own hand; and Lupin is killed at the
lexicon.org/thing/great-battle-hogwarts/">Battle of Hogwarts. That’s enough death to launch a Chinese superstition right there.
The Potters and the Longbottoms had both thrice defied Voldemort and the Death Eaters. It was their fateful fourth encounter that proved to be their downfall.
Harry lives with the Dursleys at
lexicon.org/place/great-britain/england/surrey/little-whinging/privet-drive/number-four-privet-drive/">number 4, Privet Drive, and we all know how unhappy Harry was there. He becomes the fourth Triwizard Champion, an event that almost ends in his death.
Multiply four by the friendlier number three, and you get
lexicon.org/2018/05/12/number-twelve/">12, a much more auspicious number.