The overall question is:

I spent the last month learning the foxtrot and waltz from a Social point of view (Very Layback,) which they did to get me interested I guess. Now I have been switch with a new teacher who show me a the technical way of dancing the foxtrot and waltz which consist of my feet pattern being changed. Now I understand that you will have to change a few things to sharpen your skills but I feel like the first teacher instructed me wrong and I have been practicing and developing incorrect muscle memory.
It now make me wonder how many other step am I going to have to relearn because I was taught a "layback" version of it?

I,m guessing that you were taught a " social " style of F/trot , resembling a Q/S , and then shown the more extreme variety of the comp. style.

They both have their uses and value, as you will begin to see.. if you are learning as a beginner, the Social standard was modified for those who were not interested in Medal tests or comp. style, and it is currently the most popular style in many countries.

The W.. T..and Q/S do not deviate nearly as much at the social level.

Yes, the social style is how they are teaching me and I am getting very frustrated with it. It does not have the technical desire that I am after. I know I am a beginner with less than two month training. But I am very much interested in the medal test or comp. style however they claim that I have to learn the social style first.

Then when they turn around and teach me a little of the comp. style that where my frustration come in. I not sure why I am putting in the extra hours of practice to find out that my pattern are incorrect to my goals.

I would think teaching me the comp. style would be more interesting and I can always tone it down if I was to teach someone else aka Social style.

So is it really best to learn the social style first or the comp. style?

Actually, this is a very interesting thread.
I've lectured first year, third year and final year students over a long period of time . During that time I've also been through the dancing learning phase (from beginner up to competition pre-champ level)and i 've leant a lot about my teaching/lecturing skills from my experiences learning to dance.
I've thought about this 'un-learning' situation a lot because i've had the same thoughts as drscience.
The way i currently view this is as follows:
1)You can't teach 4th-year material to 1st-year students
2)Understanding of new information is built on previous knowledge and experience, and the better this previous knowledge, the faster you will learn new material. So very good basics are important.
3)Never knowingly teach anything which is wrong or bad technique.
So for example, you would go to some trouble to make sure a beginner closes feet correctly in slow waltz (where it's needed of course), keeps good timing and avoids poor posture. These are serious fundamentals.
Competition dancing is an adaptation of good social dancing but the basics are the same.

Social " basics " have little in common structurally with for.e.g. F/Trot in the Intern social style ( American standards apart )

The reason the International style is more adaptable, is primarily because we may use the basic bronze/ silver format at a social AND competitive level with little change in concepts other than the variety. We do not however, use the " social " standard as a comp. division, wherein the Americans do.

having worked with both levels for multi yrs, as a teacher, coach and examiner, I must confess ,that my personal belief is the Amer. standards, socially, are superior in content and design, to their english counterpart..

The social levels of both Amer. and Intern style have many similarites.. the major difference is the departure that Amer. Silver takes., thru re structuring of the "open " footwork approach .