Small wouldn't be the word I would have used. It's actually the same as countries such Netherlands, France, or Austria, and it's superior to Germany, Switzerland or Belgium.
In any case this has been in debate for years, usually opposed by the People's Party (PP) with the argument that the current Spanish Financial Crisis does not allow an extension. In a 2016 article of El Pais (English version) you can read (Note: CEOE is the Confederation of Employers and Industries of Spain):
According to the figures, between January 2011 and December 2014,
Spain saved more than €500 million in maternity and paternity leave as
a result of the falling birth rate, spending just €1.6 billion in
The PP accuses its rivals of making promises it cannot keep. The CEOE
business confederation is also opposed to extending paternity leave,
saying it will hit businesses hard. “Often, businesses have to pay
social security while somebody is absent, and it creates
organizational problems because that man has to be replaced
temporarily,” says Jordi García Viña, the CEOE’s labor relations
Spain has had a drop of almost 13% in birth rate since 2008:
Spain is ageing in step with the crisis. The collapse of the job
market, wage cuts and lower expectations for future prosperity are all
causing birth rates to dwindle. Since 2008, the year when the impact
of the recession began to be felt, the number of births has fallen
nearly 13 percent, according to data released last week by the
National Statistics Institute (INE).
For that reason, quite recently, the dimension of the problem has prompted PP and Ciudadanos (en: Citizens) to agree in extending the parental leave:
Ciudadanos ha acordado con el PP, en el marco de las negociaciones de
los Presupuestos Generales del Estado (PGE) para el próximo año,
ampliar una semana más, hasta sumar cinco, los permisos de paternidad
a partir de enero de 2018.
My Spanish isn't great but it seems to say that PP and Citizens have agreed in extending the Paternity Leave by one week starting January 2018 (so things should be changing as we speak).
NOTE: SJuan76 called my attention to the fact that the extension is indeed exclusive to paternity leave as opposed to maternity leave or the gender parity term parental leave. As so, as we speak, the OP number for 16 week of maternal leave is still very much in place.