I think that there are several jobs that we do not need to outsource. We should try to keep as many jobs available here as possible, but there are some that should do no matter what. Pizza delivery sounds like one. Intelligence gathering is another. Teaching would be a third.
As companies drive for higher profits by outsourcing things like customer service, it's a given that the quality of the service declines. But companies are willing to take greater risks if it adds higher profit. There will always be jobs in health care that can never be outsourced. About any other job that isn't supplied directly to the customer, such as restaurants, hotel service, or auto mechanic, runs the risk of getting outsourced.
There are a ton of jobs that can not be outsourced. Namely, service jobs are generally impossible to outsource. Plumbers, electricians, emergency workers, teachers and mail carriers are some examples of jobs that are all but impossible to outsource. These jobs require someone to be physically there to do the work.
You cannot outsource a job that requires being physically present. This is not to say that those jobs won't one day be roboticized. For example, you cannot outsource the pizza delivery driver's job to India. However, you can replace the pizza delivery driver with a self-driving car or a drone. In the end, it is hard to think of any job that couldn't conceivably be done mechanically; the same can't be said for outsourcing.