Arguments every creationist should know:
1) Global flood destroys the belief in billions and millions of years. You can't have both. If there was (and there was) a global flood then the earth is young. Various lines of evidence support the global flood. Including ancient documents and histories from over 200 cultures.
2) Conflicting dating methods. Absolute dating methods using radiometric isotypes do get deep time dates. But they are in conflict with each other and are in conflict with other dating methods. There are many examples where samples of known age have been given incorrect ages millions to billions of years out. If the rock layers surrounding a fossil say its hundreds of millions of years old, but the carbon dating on the fossil, not rock says its only thousands, you have serious reasons to doubt their proposed millions of years.
3) Unfossilized fossils have been found. Fossils over a million years old can not have un-fossilized remains in them. The fact that there are many that do, show empirically fossils are not millions of years old.
4) Carbon dating has been used to test coal, diamond, un-fossilized dinosaur remains and returns ages not consistent with evolutionary time scales. (Thousands of years not millions). Which means all coal deposits, dinosaur deposits are young, not old.
5) Body plans for most of the phyla in the taxonomy classification were not supposed to be present in the lowest layers and supposed oldest layers of rocks. But they are.
6) Intermediate fossils are missing. Why is there not a blur of creatures? Not just a few missing links, but millions of missing links showing gradual changes. Why are there identifiable animals and not a blur of crossovers with billions of variations which is what we should see if creatures evolved? But what we have is creatures even a 5-year-old can differentiate from each other.
7) Irreducible complexity, examples of machines and processes are constantly being found in biology. These systems, processes show there is no step-by-step way they could be formed. Each component or process needed to be in place for these to work. A chicken and egg problem exists. There are many examples of these. Which show evolution could not have created them.
8) Instructions and information are found in every living creature. But information theory shows information only comes from a mind, and can not be generated by natural processes. So the coding in DNA to create proteins can not be accounted for by the natural explanation Darwinists claim.
9) Genetic Entropy is occurring in all genomes, plant and animal. Mutations are building up, and at the current rate of decay, all life could not be more than the 10 000 years old. Neutral and harmful mutations are overwhelming any rare beneficial mutations and are being stored in the genome and natural selection is incapable of detecting them. This is leading to genetic meltdown and extinction. Each offspring is passing on genetic errors which increases the genetic collapse. Tracking back with empirical rates of mutations observed, all plant, animal and human life could not be old. (thousands of years old not millions)
There are many more arguments, but these ones are quite popular with loads of supporting evidence to back them up.