I don't think any instructor (at least that I am aware) says, "what are you here for" as the first thing they say.
It seems that most instructors I know, first ask the name, where they live, and maybe what they do. And somewhere after that ask what would you like to get out of the lesson. And sure, most say something like "Parallel better", "ski better", "ski bumps", "to stop", etc. It seems like a no brainer perhaps. "duh, why are you asking me. Your the instructor, you should know." What I as an instructor am looking for, is a desire. And a little specific knowledge. Is this your first time on snow this year? Lessons in the past? etc. I view one of the jobs of an instructor, is to create a road map (via excercises, example, guided mileage) that will lead us in that direction or to the achievement of the desired outcome
Here is a true story you may find amusing.
Jackson Hole- (one of my favorite places to ski in North America)
My wife MADE me take a lesson (I was a Lvl 3 instructor at the time), and I was looking forward to it. I did not tell them I was a Full Certified instructor, nor was I asked. I am placed in the Lvl 9 lesson. 15" of fresh had fallen the night before. The instructor took us to the nicest groomed run on the mountain and we began to learn carving. I went along willingly, and had fun. Except I was longing for the fresh stuff though. At the end of the morning we made it on the tram. About half way down as we were heading down to the lodge. I asked the instructor if I could ski the 2000' vert of untracked fresh. Fortunately he said YES, but the rest of the group didn't follow, but I met the group for lunch.
After lunch, the instructor asked another instuctor to join the group. The New instructor, asked me if I would like to have a Lvl "10" lesson. We bid a friendly farewell to the group. He asked me "What would you like to get out of the afternoon". "Ah, now your talking". I answered, "I want to ski where you ski on your day off". Up the tram we went. After a top to bottom, he asked is that what you are looking for? I answered, "yep, but could you show me how you introduce a lesson of which the objective is to jump into Corbet's?"
He then led me through a 4 jump progression with coaching specific to jumping, landing, and skiing out of Corbet Couloir.
Great day. A cash tip for both instructors. The tip for the first instructor was for putting his ego aside and notice I had different goals for the lesson. And a tip for the second, was for asking me what I wanted to do today. And lastly, a smile and a fond memory for me. Because I relized I need to know what I want to get out of the lesson, even though I didn't know how to get there. Well done, JH ski school.