The 5e PHB is explicit that orcish traits of evil and savagery are caused by nature, not nurture:
The one-eyed god Gruumsh created the orcs, and even those orcs who turn away from his worship can't fully escape his influence. The same is true of haIf-orcs. Though their human blood moderates the impact of their orcish heritage...
The evil deities who created other races, though, made those races to serve them. Those races have strong inborn tendencies that match the nature of their gods. Most orcs share the violent, savage nature of the orc god, Gruumsh. and are thus inclined toward evil. Even if an orc chooses a good alignment, it struggles against its innate tendencies for its entire life. (Even half-orcs feel the lingering pull of the orc god's influence.)
The 1e DMG takes the same view. The text suggests that if a half-orc does not possess negative traits, it is because they favoured the human parent:
Half-Orcs are boors. They are rude, crude, crass, and generally obnoxious. Because most are cowardly they tend to be bullies and cruel to the weak, but they will quickly knuckle under to the stronger. This does not mean that all half-orcs are horrid, only most of them. It neither means that they are necessarily stupid nor incapable. They will always seek to gain the upper hand and dominate those around them so as to be able to exercise their natural tendencies; half-orcs are greedy too. They can, of course, favor their human parent more than their orcish one.