Hair on the head does not have an unlimited length. All hairs, regardless of location on the body, go through three growth phases. In the anagen phase, the hair is actively growing. Human scalp hair typically grows about a centimeter a month during this phase, which can last anywhere from 2 to more than 6 years. The length of the anagen phase determines the maximum length to which one's hair will grow.
At the end of the anagen phase, the hair follicle enters the catagen phase, during which the hair stops growing, and a club-shaped "root" forms on the end of the hair. This is a short phase, lasting less than a month, and is followed by the telogen phase, a time during which the hair follicle rests. The telogen phase lasts about 3 months for head hairs, and longer for body hairs. At the end of the telogen phase, the hair falls out and the follicle re-enters the anagen phase.
Since hairs are in all different places in the cycle at any given time, you usually don't notice the process occurring.
Hair length is controled by active hair follicle. So the hair follicles on top of your head might be active growing hair called the growth phase, then take a rest called the rest phase.
So arm hairs have much shorter growth phases than your head hairs, that keeps arm hair relatively short. But not in all people.
Some people can have very long arm hairs. Their hair follicles are programmed a little differently the growth phase is longer.
So it depends is the active and inactive hair follicle.