Bronze,
I feel you are getting so much information your head must be ready to explode.
MY head is ready to explode and I already know how to both lead and follow the cross and have taught it!
Bronze, don't make yourself nuts. Take a few more lessons with this instructor and see where they go with things.
Some instructors start off with a basic pattern that leads to the cross simply so people can feel they are getting somewhere and have something to build on. Its easy to spend the entire first hour standing still or only walking a little because dealing with all the technique up front takes time. A lot of students feel gyped when that's all they do for the first lesson or even the first few lessons. This is especially true of a clientele that is taking or has taken other partner dance forms, and teachers who get those students know that's how they're going to feel. Nobody spends the first fox trot or swing lesson talking (about concepts) more than moving.
If after a few lessons, it seems you are ONLY getting patterns and no instruction on the fundamentals that make EACH ELEMENT of the pattern work, then look elsewhere for instruction.
But there are teachers who don't get bogged down in that in the first lesson or two, because people want to dance and move! They come to dance classes to have fun and explore a hobby... they don't know yet that its a way of life (for some of us, an addiction!), and sometimes its better that they don't realize that too soon!
I know a teacher who starts off in lesson 1 with basic milonga. Step on every main beat, change feet with every step,
keep moving! He gives a simple basic 6 count pattern and maybe several simple variations of it depending on how things are going. At the end of lesson 1, folks think they learned something and they got to move around a lot. They're tired and they feel good. They won't remember all of it, but they'll come back because they had a good time and want to go further. They may even joke about the "cartoon character" music (never thought of milonga that way til a student said it.. now I always think.. yep... it does have that quality a little bit!)
They don't leave thinking... "Oh my God this is going to take FOREVER!" which may be just about the
worst thing for a student to feel after their first lesson.
He tells them that there are 3 basic AT dance forms (milonga, tango and vals) and that today we are playing with milonga and we'll get to the others in succesive lessons. He sneaks in fundamental concepts about floorcraft and line of dance. He sneaks in rotating the shoulders to walk outside of the follower and how to stay connected. He talks about posture, holds, forward pressure, staying in front of the leader (for followers) moving directly into the follower with clear intention instead of worrying about stepping on her (for leaders) and the method of reaching (stepping, walking, whatever) for both leaders going forward (chest leads, not feet!) and followers going backwards (no falling back... stay forward!) He gets people listening to and dancing to the music rather than thinking about some intricate pattern using "tango'ish" movements that aren't intuitive or easy for non-dancers (and that typically are hard for beginners to fit into the music)
Yep... all in lesson one while actually doing lots of really energetic dancing. And it works. All those principles get reinforced in every lesson AND people get to actually dance around the room. Its LIVELY. People don't even realize that the pattern was pretty simple cause they felt like they were DANCING.
He delves into tango rhythm and putting in the cross and some of that other stuff a few lessons down the road, still hammering the fundamentals from lesson one into everyone's head. And he doesn't expect people to get the cross in only a lesson or two, but since its such a common piece of the tango vocabulary, it gets worked on even when the lesson is about something else. He introduces it fairly early (maybe at the end of one of the first lessons as a preview of coming attractions) because it feels "tangoy" to people. The things that make it complicated or difficult are dealt with in
stages as people progress rather than as a "move that we learn this week".
My point is... don't make yourself nuts. This really is a way of life. A huge time commitment is nessesary to become profficient at tango. Look for an instructor who tells you the HOW and WHY behind the elements of the patterns they give, but also figure they might not want to scare people off with too much of that in the first couple of lessons. If you haven't gotten any of that kind of thing by lesson 3 or 4, I'd say you're not going to get it and its time to find someone else.