'if men are better at spatial awareness why aren't they typically stacking small cupboards with weekly shops?'
because people do things if they get enjoyment or perceive that they will get rewards from doing them. Just because someone has good spatial awareness doesn't mean that they will want to stack cupboards. If they have a choice, they may not like doing that.
'If women are better at interpreting simultaneous complex visual signals (empathy from faces is this, unless you belive in telepathy) why aren't they typically air traffic controllers and football managers?'
I think women are better at reading human emotions and interpreting body language and facial gestures. This is not the same as looking at blips on a screen. The difference is the complex understanding of human nature and emotion. There is probably no advanatge for either sex in reading blips on a screen. We don't live in a neat world where the best person for a job is the person that does the job. There are other factors such as whether people want to do that job, whether there are barriers which prevent them entering that profession etc. Being a football manager is about more than reading people's emotions. It involves having a deep understanding of football tactics and understanding and empathising with the players and being able to gain their respect in order to manage them.
'And if they are better at 'nurturing' why not Army training instructors?'
I doubt that army training instructors are about nurturing.
'if they have lower boredom thresholds (S B-C uses this to explain housework) why are so many traditional male jobs in hevay industry repetitive and boring (much more so than housework)'
because these men don't have much choice in the type of work that they do. They have to take what is on offer. They can't afford to turn the jobs down just because they are boring.
'A man walking towards you raising his fist and shouting incoherently because drunk is communictaing as effectively as a woman mediating-both are letting others know what they feel.'
but the drunk raising his fist is not the type of communication that is required for business. To influence people, manage staff and win customers, a much more understanding human empathetic communication is required, and women on the whole are better at that.
'to go back to my first post-why then are newsreaders or PR execs not predominantly female?'
With newsreaders teh TV companies usually like to try to create a balance. A lot of women do work in PR. But again jobs don't necessarily go to the best candidates, there are other factors involved.
'And why, given modern politics is about election and communication, are politicians not predominantly female?'
because politics is essentially about power, and men are often attracted to these roles. Politics is about much more than communication and spin.