the first big problem for naturalists is the problem of spontaneous generation.it is basically impossible. the odds are so slim you cant even call them odds. 60 billion to 1? really? thats like trying to find an individual grain of sand in all of the gobi desert. the odds are way to much against them for it to even be plausible. this is just the odds for creation of life from no life. this isn't even scratching the odds that this life created some how evolved into a human. this is the belief in macro evolution, or belief in big evolution changes. like a bird having the capability to eventually becoming an elephant. this is just one of the three big flaws that deny a naturalistic beginning.
the second is random mutations. mutation means a change in the chromosomes in the DNA . the problem with this though is that mutations are usually a bad thing. and if natural selection is all about destroying the weakest link then wouldn't a mutated animal be immediately destroyed? take the fly that grew a second set of wings. at first glance this second set of wings would be a good thing and make it stronger. but the wings don't even function. thus weighing it down and making it fall short of the other flies and die. this is an example of why natural selection cannot be.
the third is that the worlds age cannot be determined. scientists who believe in naturalism argue that the earth is billions of years old. they state that it is this old because of carbon dating done on sedimentary rocks. the fact of the matter is that after mount saint Helens erupted rocks were recovered that would carbon date as if they were millions of years old. but in reality only took 20 years to form.
