Certain orchids are impossible to cultivate. My state's (MN) flower, the Queen Lady Slipper, has notoriously resisted cultivation thus far. It rarely germinates from seed, preferring to spread vegetatively. It's thought that the conditions necessary for it's germination are very specific to its natural environment - wetlands and bogs. It also takes a decade or more to mature and flower from seed, though it can live for up to 50 years. It's such a precarious and sensitive flower that it is a state crime to destroy or uproot them. I remember my grandparents had a small colony of them growing on their property by a lake up near Nisswa when I was a kid. They surrounded it with a locked fence, with a sign that read, "It is illegal by state law to pick a lady slipper flower. Anybody caught picking this flower will be shot and then prosecuted."

One thing to consider about mushrooms is that they represent a mere fraction of a much larger subterranean organism that exists in a balance with its host substrate. Some fungi are not picky about their substrate and are thus easier to cultivate. Others require a very specific substrate and growing conditions that are not currently possibly to replicate artificially.