Selection implies a selectorOne problem with using the term "selection" is that it fairly strongly implies a selector.
The "selection" terminology arose from generalising "artificial selection" to "natural selection". Artificial selection makes reasonable sense - because there's a human selector doing the selecting, but with natural selection there's often not a selector. Talking about "natural selection" represents a kind of "agentification" of nature.
Of course sometimes there really is a selector. In female choice, agents do literally select their mates. However, if an asexual bacterium divides, there's not really any selecting agent - the environment.
Agentifying nature is not a dreadful problem.
Survival or death?The selection terminology seems kind-of ambiguous about whether individuals are being selected for survival or death. In some respects this is appropriate: sometimes mates are selected for sex, sometimes they are selected for rejection - and natural selection is often selection for death. However the use of selection coefficients makes it plain that selection is a positive force - indicating what is retained. However, the grim reaper obviously doesn't work that way. Death has a blacklist - not a whitelist. This mixture of ambiguity and wrongness seems rather confusing.
Is nature even choosing?The term "selection" pretty strongly implies choosing between alternatives. However it is not always clear that that is what is going on. Nature doesn't so much choose organisms as score them, expressing its approval with a certain number of offspring. A score can be represented by a series of selections, but it's a bit painful. Also, when generalising Darwinism, more problems along these lines arise. New genomes can be made by extrapolating or interpolating. Consequently, the next thing to try may be something not tried before. Such cases are poorly described as being "selections".
Organism disempowermentIt has been said the idea of nature "selecting" makes the organism seem impotent. Rather than the organism being rated by its environment, organisms rate their environments, and if they don't like them they migrate to new ones. This perspective puts the organism more in charge - rather than picturing organisms as being at the mercy of their environment.
AlternativesThose are the alleged problems that I have heard about. I expect most readers will find at least some points to sympathise with.
John Wilkins has proposed "sorting" and "filtering" as alternatives that avoid agentifying nature.
"Culling" is a term that could be used to refer to "selection by death".
None of these really provide a term suitable for use in a generalised version of Darwinism. Generalised Darwinism still normally features gradualism, but there, it seems difficult to go far beyond vague terms like "modification" or "adjustment" - e.g. "the heritable information was slightly modified". Such vagueness may be accurate, but it isn't very catchy.
The other thing to say is that "selection" terminology has huge inertia - and a failure to use it would probably hamper communication with many readers.