As long as we are picking nits, it almost certainly isn't a profession in the classical or even legal sense except for doctors and nurses supporting the effort (and the odd attorney, cleric or engineer) . It may well be an occupation or even a trade. But not a profession.
While I can't believe I'm even replying to this...
Let's look at some dictionary definition of "profession"
pro·fes·sion
[prəˈfeSHən]
career ·
occupation ·
calling ·
vocation ·
métier · line (of work)
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noun
1.
a vocation requiring knowledge of some department of learning or science:
the profession of teaching.
Compare
learned profession.
2.
any vocation or business.
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profession(noun)
an occupation requiring special education
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An occupation or career: "One of the highest compliments a child can pay a parent is to choose his or her profession"
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While I whole heartedly agree that doctors, lawyers, etc are in a profession I disagree with saying that other fields/work are not. That's very "elitist" to say the least.
It's true that many in SAR are doing it as more of a part-time gig but there are many who are fully engrossed in this field and "Do It" to the level of doctors and lawyers. Years of study, training, certifications, and more just to be "on call" waiting for someone in need.
If you think for a single moment that that Alpine SAR, THAARP, and HARR are not professions that need lots of training, credentialing and certifications you are seriously mistaken. Not every SAAR member looks at it as a profession there are many out here who are genuinely in the SAR profession.