I'll take a stab at explaining to you why your teacher is being anal retentive about showing every single step. And, it has a lot to do with testing into remedial mathematics. Now, perhaps things are coming back to you more quickly than they are to other students, but the teacher has no way of knowing that. But, I'll give you an example I experience all the time:
I can ask students in high school to add 2/3 to 5/7. Amazing how much some struggle to get the correct answer, but for those struggling, a simple, "how do you add fractions together" generally elicits a response of "get a common denominator." Okay, go ahead. Those students will then say "multiply the first fraction by 7 and multiply the second fraction by 3." And, they'll stick a 7 in front of the first fraction and a 3 in front of the second fraction, and then write 14/21 + 15/21 = 29/21. Then I ask, "why did you multiply by 7?" "To get a common denominator." "But, if you multiply by 7, wouldn't that make it 7 times as big?" "I dunno, that's how we were taught to do it." (No it wasn't.) But, for these students, they memorized procedures and didn't know the concept that allowed them to do what they're doing. In this case, in case you haven't figured it out, NO, you don't multiply by 7 and 3. You multiply by 1 and 1. Though, 1 is in the form of 7/7 and 3/3. Multiplying by one (identity property of multiplication) doesn't change the value of something (though it might make it look a little different.) So great. They can add two fractions together, have no idea why their procedure works, but JUST LIKE YOU, they get the correct answer, so no big deal, right? Well, when they get to a little higher mathematics and they encounter something like sinx (cosx/tanx) They wind up with (sinx cosx)/(sinx tanx) because when something's out front, don't you multiply it by the top and by the bottom? That's what they've been doing all along! *(Just as in class, the words that come out of my mouth are numerator and denominator, though I write top and bottom as I'm saying those words, out of laziness & for the sake of time. Trust me that I was thinking "numerator" as I typed "top.")
"What you do to one side is what you do to the other side" is perhaps the MOST important rule in mathematics. It's amazing how often people do not apply it, because they're attempting to memorize procedures, rather than apply such a simple concept. For example, take the equation (log meaning log base 10):
log(x+2) + log(6x+2) = 2. I can't count the number of times I see (x+2) + (6x+2) = 100. "What did you do?" "Don't you do 10^ to get rid of log?" "No, what you do is always this: 'what you do to one side is what you do to the other side.'" So, it's 10^[log(x+2) + log(6x+2)]=10^2. Inevitably, I show them that it's easier to combine logs first, then eliminate the logs, though they can do it their way which still results in a product, but that's a bit beyond the OP's needs, suffice to say, OP, while you may think it's trivial, and while you may be well beyond the ability of the students in class but you were simply rusty during the placement exam, you tested into a course that's generally dominated by students who do NOT understand the concepts & are thus limited in their ability to do any higher level mathematics correctly.