Why gossip is such a stubborn puzzle
Gossip is easy to observe and hard to account for. People everywhere talk about absent others, often at some cost to themselves and with no obvious direct payoff. A game-theoretic model proposes an evolutionary cycle to explain it: spreading information about people's reputations leads more individuals to condition their behavior on those reputations, which in turn pushes people to act more cooperatively toward gossipers to protect their own reputations [3]. In that account, gossiping gains an evolutionary advantage and spreads, and the spread reinforces the two functions, reputation dissemination and deterrence of selfishness [3].
The key point is that the explanation is a proposed cycle, not a settled cause. The authors describe the evolution of gossip as a puzzle and present their model as a way to assess their proposed cycle [3]. So gossip is difficult not because no mechanism can be imagined, but because the mechanism has to connect a private social act to a public evolutionary benefit.
Purposeful behavior resists a clean evolutionary story
A different kind of difficulty appears when the feature is intentional. Work on economic theory notes that purposeful behavior is hard to reconcile with evolutionary approaches, and that the neo-Darwinian synthesis explains evolution in biology in ways that do not straightforwardly accommodate intention [2]. This is a conceptual tension rather than a missing fact: a trait that seems aimed at a goal sits awkwardly beside a process usually described without goals.
That paper also suggests some previously difficult features may become tractable once intentionality and multi-level processes are taken into account [2]. The difficulty, then, may lie less in the feature itself than in the framework used to describe it.
Some difficulties are about explanation itself
Earlier writing on emergent evolution frames the problem at the level of explanation. Its abstract refers to difficulties that arise when accounting for certain features, and to how a thinker grapples with a cardinal feature [1]. The available summary does not identify a specific trait, so it supports only the general point that some evolutionary phenomena were treated as genuinely hard to explain [1].
Taken together, the evidence points to two different senses of "most difficult." Gossip is a concrete behavior whose evolutionary path is still described as a puzzle [3], while intention and purpose pose a conceptual mismatch with evolutionary theory [2]. Which counts as hardest depends on whether you are asking which behavior is hardest to model or which kind of feature is hardest to fit into the theory at all.
Sources used in this answer
Emergent evolution
The paper discusses difficulties in explaining evolutionary phenomena and treats certain features as hard to account for.
Evolution and intention in economic theory
Purposeful, intentional behavior is difficult to reconcile with evolutionary approaches in economic theory.
Explaining the evolution of gossip
Gossip is ubiquitous in human societies, yet its evolution remains a puzzle; a model proposes it spreads through a cycle linking reputation dissemination and deterrence of selfishness.