How was Paul a Roman citizen if he was an Israelite? And why did it matter?

During New Testament times one could become a Roman either by birth, by purchasing the right to be one, or through at least 25 years of military service. As Paul stated in Acts 22 he was born into Roman citizenship.

According to BibleStudy.org, “Roman citizens had the . . . ability to request Caesar himself hear their case. Additionally, citizens could not be tortured or whipped (scourged), nor could they receive the death penalty, unless they were guilty of treason. It was this right that kept the apostle [Paul] from a severe flogging at the hands of Roman soldiers (Acts 22:23 – 29). Paul used his right to a trial before Caesar in Rome in order to avoid being tried before religious leaders in Jerusalem who hated him.” (Source)