What are the highest skill level jobs that can't be outsourced?

I am going to proceed from the assumption, that by ‘outsourcing’ you mean ‘offshoring’
Right now, Research and Development. That is where the West still has the edge.
But if you neglect, and in certain countries even dismantle, education and science, that, too, will soon change.
Apart from that, there is domestic infrastructure construction and maintenance, general construction (buildings), retail, goods transport, public transport, medical services, police, and government services.

If the TPP passes, the US Presidency itself might be outsourced! ;-o

It’s all students from China over here doing the research though.

They are basically not maintaining the infrastructure here at all. It all looks fine and dandy because they’ll repaint and repave but just below the surface it’s all rotting away.

Basically we are just building new strip malls and starbucks but the design is outsourced and illegals do the work.

Lots of blue-collar jobs like diesel mechanics, miners, heavy equipment operators, explosive handlers.

In the US, lawyers can’t practice in states where they aren’t admitted to the bar or their home state has a reciprocal agreement.

This won’t change soon, because you-know-who writes the rules.

Outsource outside of the company or hiring off shore?

president