These are crude jokes but lots of people laugh about such jokes, especially men (from all classes). I've seen a million of such 'lad jokes' on facebook and there is nothing wrong with it, unless you belong to a royal family and the subjects of those jokes are your own family members. In general I would say that everybody would be embarrassed in some kind of way if private emails were made public for others to read, especially over a long time period.
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In a way you are right that these emails fall under the "lad jokes" label.
But very few men make these kind of jokes about their own family members.
And in my experience, especially vis-a-vis women, men make these kind of jokes when they feel threatened or insecure. That is when misogyny rises to the surface in order to reduce the powerful female to her most basic body parts/sexual function.
Inaki, in choosing to make fun of Letizia in this manner, betrayed his own inadequacies and insecurities, rather than Letizia's.
Finally I find this whole scenario very illuminating.
On one hand some of us have been unable to get past Letizia's "Let me finish" remark during her engagement.
10 years have gone by and we still rake her over the coals for that....we still extrapolate to nth degree and label her as attention seeking, wanting to overshadow Felipe, not knowing how to be princess etc...when all her actions since her engagement have been anything but. Same goes for her sisters. One only has to look at what Telma had to go through when she came back to Spain to have a baby.
On the other hand, we have been able to laugh off, brush off, ignore many more significant transgressions by Cristina and Inaki. This email being the latest example. Inaki has fallen off the pedestal only when things got really serious with the Noos case.
Even knowing all this, we still find Letizia at fault when there is some distance between Cristina and Letizia at a family gathering.
My post is not intended to be Inaki vs Letizia. But more about how we differently we have reacted to them.
PS: My heart goes out to posters who fell for Cristina and Inaki's "golden couple" image. These revelations must have been painful. I would hate it if their was a similar dichotomy between the "marketed image" and "real image" of Letizia and Felipe.