The standard error of the estimate is too small. When variables are highly correlated, the ones that appear in the model are just a matter of chance and can change with the addition of one or two more observations. The procedure for generating the model must exclude observations that are missing any of the potential predictors. However, some of these observations will not be missing any of the predictors selected for the final model. Sometimes predictors in the final model are no longer statistically significant when the model is fitted to the larger data set that includes these set aside observations.
Some analysts soldier on regardless and look for consistency among the methods.
They gain confidence in a model if most every method leads to the same candidate. Perhaps there is some justification for this belief. I have rarely seen most every method lead to the same candidate. It would be tempting to say that, these criticisms notwithstanding, model selection procedures are useful in suggesting lines of further research. Perhaps they do.