Why can't they be both a transitional species and individual extinct species?
Perhaps you are confusing the words "transitional" and "ancestral"? This is a common misunderstanding. When we say that a species is transitional we are making no claims of direct ancestor-descendant relationships. Transitional simply means having a mixture of characteristics between an earlier species group and a later species group (i.e. a mixture of characteristics between two taxa). Fossils don't come with birth certificates, so we don't make strong claims of direct ancestry. However, fossils do come with morphology, so we do use morphology to see how they compare to other species.
So to answer your question, a transitional fossil can be an extinct species. It can also be an offshoot of the direct ancestral line between modern species and a more distant ancestor. Darwin himself discussed how "collateral" descendants can be used to infer evolutionary pathways:
"In looking for the gradations by which an organ in any species has been perfected, we ought to look exclusively to its lineal ancestors; but this is scarcely ever possible, and we are forced in each case to look to species of the same group, that is to the collateral descendants from the same original parent-form, in order to see what gradations are possible, and for the chance of some gradations having been transmitted from the earlier stages of descent, in an unaltered or little altered condition."--Charles Darwin, "Origin of Species"
The Origin of Species: Chapter 6
Of course, separate creation of species will also result in species that have a mixture of features from two divergent taxa. So what is the real test here? The test is that the theory of evolution predicts that transitionals should fall into a nested hierarchy. For separate creation, there is absolutely no reason why we should see a nested hierarchy.
So what do we find? We only find the mixture of characteristics that the theory of evolution predicts we should find. We find dino-bird transitionals, but not bird-mammal transitionals. We find ape-human transitionals, but not ape-dog transitionals.
Also, we don't test theories with evidence we don't have. That is why the whole "missing fossils" argument fails right at the start.