Imagine that there are people:
who are claiming that Software Testing is not a profession.
who think Software Testing is just an activity within another profession.
who think that anyone can test software.
If software testing was not a profession. How would we call it then?
Is it an activity? At least Wikipedia leads to a list Activity which give some definitions, and also giving a list that they called: "This disambiguation page lists articles associated with the same title. If an internal link led you here, you may wish to change the link to point directly to the intended article."
One of the definitions is Task. So, is it a task? Wikipedia defines Task as "a task is part of a set of actions which accomplish a job, problem or assignment."
Of course Software Testing can be part of another profession using this definition. For example: when you are a developer, testing should be one of your tasks.
I think when a set of actions is becoming to complex it can be defined as a specialism. If a specialism results in an isolated set of actions it becomes a profession. As the initial tasks are not performed any more. The focus shifted from programming to testing.
According to Wikipedia Profession can be defined as: "A profession is an occupation, vocation or career where specialized knowledge of a subject, field, or science is applied"
I think Software Testing fits in this definition. As you can specialize yourselves in testing and also in different areas of Software Testing. Which makes me wonder why is developing thought extensively on schools and Software Testing is just a subject of Development? Do other see my profession differently then I do? Therefore I wonder what else is Software Testing? Or should be deal with this profession as we deal with other professions? I think we should.
Nowadays you see Agile and SCRUM as development methods are used. They are based on working with teams and with team responsibilities. This gives the opportunity for the tester to program also. Developing becomes a task of the profession of Software Testing and is not a profession anymore. Testers have to learn how to program during their education.
Now you see that the circle is round. A set of actions can be called Testing. Testing can be seen as a task. A specialized set of tasks can result in specialism which can be identified as profession. The content of a profession can be increased with new activities. Increasing the content of a profession might lead into a new profession or fit into an other profession.
Perhaps the answer on the initial question: "If Software Testing was not a profession how would we call it then?" is based on the starting point and your goal. If you start as professional tester, you can call it a profession. If you start as developer, it is a task. Observe how your profession is growing. Your profession might change over the years.