There is some confusion out there in regards to a person's genealogical makeup vs their DNA makeup. You frequently hear people say they're half German and half Irish, or a quarter Polish, a quarter German and half Italian or some such makeup in regards to their genetic and/or ancestral origins. For most people who make these statements, they don't make a distinction between the two or even think there is a difference. In actuality, there is an enormous difference between your ancestral origins and your genetic makeup.
Yes, you can definitely make the statement that a quarter of your ancestors were Jewish, for example and this may be true as far as you can tell. Really though, do you know what percentage of your ancestors were a given race beyond the most recent three to ten generations? Further back than that, you certainly can't tell that for sure for the vast majority of your ancestors. Even more than that though, the way your genetics get passed down to the next generation, you tend to lose most of the genetics of the majority of your ancestors after just a few generations. Here is a simple example to illustrate.
Take two parents who have a child. In this illustration, the mother is about three-quarters showing in the lime green color. Let's say this is her Irish ancestry. About 3/8 of her ancestry is showing as German (brown) and the last roughly ten percent shows up as Jewish (lilac). The father is a little more than a quarter East Indian (red), a little more than a quarter African (dark blue), a little more than quarter Oriental (purple) and a little less than a quarter as Italian (light blue).
Their son gets half of his genetics from each of his parents. Exactly which pieces of genetic code received from each parent is random. In my example, I simplified it in that he got the left half from his father and his right half from his mother. In reality, the pieces tend to be large strings but can be very tiny pieces, down to single genetic markers.
In the example for the daughter of another couple, let's give the values received from the mother as 33% Scandinavian (pink), 33% Native American (gray) and 33% Middle Eastern (pale yellow) and from the father as 25% Spanish (green), 33% French (blue), 33% Greek (burgandy) and 10% Russian (gold). Again, the daughter is given the left half from her mother and the right half from her father.
Now, when the son from the first example and the daughter from the second example have a child, I took the 25% from each end from the child's father (the son from the first example) and the 50% from the center from the child's mother (the daughter from the second example).
The result is that the grandson has nearly all of his grandfather's East Indian DNA (red), a tiny bit of his grandmother's Scandanavian (pink), about half of his other grandmother's Native American (gray), a little more than half of his grandfather's Greek (burgandy), a little more than half of his grandmother's German and all of his mother's Jewish (lilac) DNA.
This grandson's ancestral DNA is very different from his genetic DNA. As an example, his Jewish genetic DNA makeup is twice as high as his genealogical makeup. His genetic makeup shows the exact same percentage of Jewish ancestry as his mother's even though he got no Jewish DNA from his father but he got all of his mother's Jewish DNA. On the other hand, his grandmother was 75% Irish (lime green) but the grandson got absolutely none of his grandmother's Irish DNA! If his grandmother was 75% Irish, that means his father 37% Irish and the grandson was 18% Irish. However, his DNA shows that he has no Irish ancestry whatsoever!
Now, keep in mind that this is a very simple example. The testing companies typically can't tell the difference between Oriental and Native American DNA, or German from French, typically. These ancestral categories are just used for illustration. Substitute your own genealogical origins and DNA origins for the numbers shown here and you should have a better idea of why your origins don't quite match up with what you expected.