Esta foi uma decisão de design quando o RIP foi criado: link :
A specific metric value is chosen to indicate an unreachable
destination; that metric value is larger than the largest valid
metric that we expect to see. In the existing implementation of RIP, 16 is used. This value is normally referred to as "infinity", since
it is larger than the largest valid metric
e mais tarde por que foi 16:
You should now see why "infinity" is chosen to be as small as
possible. If a network becomes completely inaccessible, we want
counting to infinity to be stopped as soon as possible. Infinity
must be large enough that no real route is that big. But it
shouldn't be any bigger than required. Thus the choice of infinity
is a tradeoff between network size and speed of convergence in case
counting to infinity happens. The designers of RIP believed that the protocol was unlikely to be practical for networks with a diameter
larger than 15.
O 15 como máximo não tem nada a ver com o tamanho do campo que contém métrica - isto é de fato 4 BYTES em tamanho (valor máximo: 2 ^ 32-1) : link
TL; DR : Acredita-se que 16 seja grande o suficiente para significar o infinito, o que torna 15 o maior diâmetro de rede possível (contagem de saltos).