Selfish genetic elements are genes or groups of genes that appear to promote themselves in an evolutionary sense irrespective of the organism they are a part of. The idea being that evolution is a competition for survival of the fittest gene and that it is the most successful genes that will gradually become more numerous and be transmitted to later generations.
Sexual reproduction is the means by which the genes of two organisms that have successfully survived to the point of being able to reproduce, are combined in a somewhat haphazard way to produce new organisms that will go on to face the trials of evolution. The fittest of these new organisms going on to recombine their genes in the next generation and so on.
As genes are the architects of the phenotypes that face the trials of evolution it is necessary that the most evolutionary successful phenotypes will have been the result of having certain genes and this will be reflected in the frequencies of the occurrence of a population's genes.
However, although it may appear that evolution is acting at a genetic level, evolution can only
act directly on phenotypes and any correlation within the genetic diversity of an organism is an indirect result of the process of evolution acting on the population of phenotypes. In the same sense evolution cannot act on groups, only on the sum of the individuals within that group. It is a logical necessity that the evolutionary fittest phenotypes will carry the genes for those phenotypes, this does not mean that the genes in any way competed in an evolutionary sense for transmission to the next generation.
It has been argued that some social insects where there are sterile workers helping to raise the offspring of relatives are examples of genes successfully competing for transmission to the next generation at the expense of the individual, sterile organism. There is no evidence that genes are competing here, in the game of evolutionary poker this poor sterile individual has simply been dealt a bad hand that happens to be to the advantage of his cousin. If evolution had given him the brains to realise what was going on he'd spend a lot less time babysitting and much more time, metaphorically speaking, at the pub with his mates. As it is, he is just following blindly his less than personally advantageous genetic programming – nothing more.
Evolution isn’t the result of competing genes, it is the result of individual phenotypes interacting and competing within an ever changing environment.
Feel free to argue amongst yourselves in the comments.