I am a student. But when I take a summer job or any other one (mostly software), I get deeply evaluated by one or another human resources professional. They run tests on me, like how fast can I add numbers, as if my application didn't show that I study maths. Then they give me grueling interviews, and look at me with piercing eyes. This is frequent. Why is this?
They look like they project that they are so much better than I. Why is it important to them? Do they do me a favor that they interview me?
What is the psychology of being a human resources professionals?
As a semi-retired partner in a professional services firm, I'm telling you that you need to check that arrogance you have, and leave it on your dorm floor. When you go to an interview, your goal needs to be to exceed expectations. Period.
I am a student....They look like they project that they are so much better than I.
In all likelihood, they are.
In my firm, the professionals who conduct interviews are our current personnel and principals who perform the job for which a candidate is interviewing. Insofar as you are a student, you can rest assured that the people interviewing you are better than you are at everything pertaining to doing the job for which you've applied. They know they are at that moment better than you, and they aren't trying to demonstrate as much to you. Regardless of whether you think so, you are the one who has something to prove, not they.
Do they do me a favor that they interview me?
For the most part and to the extent it's you and not a different individual they opted to invite to an interview, yes.
Before I sold my firm to a competitor, my partners and I did campus recruiting of MBAs and graduate economics students. We would get between 75 and 120 resumes for two positions we had available, and we'd "phone screen" about twenty-five applicants and extend interview opportunities to three to five applicants. Why? Because we didn't have time to interview more than five people.
My current firm is much larger. We receive 300-500 undergraduate applications and 200-300 graduate student applications per office (we are in every major city in the U.S. and Europe and most major cities in TROW). Typically any given recruiting event results in our interviewing about 20 people.
So, at least as far as interviewing in my firm and industry (because it's no different among our competitors) while your academic (and professional experience if you're completing a graduate degree) performance, comportment, communication skills, etc. that can be reviewed and/or gleaned prior to an interview speak for themselves, that you may be selected from what is surely a large pool of highly qualified applicants is to some extent your being accorded a favor.
Now do I and my colleagues think of it as doing our applicants a favor? No, we don't. That said, you should think of it that way because, based on the tone of your OP, you need a bit of self-implemented attitude adjustment, namely a boost in humility. I wrote "self-implemented" because if you don't do it for yourself, eventually, someone is going to do it for you, and you'll like that adjustment far less than the self-inspired kind, which isn't exactly fun, but is the better approach to personal development.