Given your premises you could predict more or less whatever you pleased, because the premise not only is false, but is impossible in our empirical universe. From false premises you can in principle derive any conclusion you please.

For a start, if a straight string had non-zero mass and were inextensible, then you had better have a good argument if you wished to demonstrate that it could be accelerated by dragging from one end at all. How would you do it without infinite acceleration?

And if you did manage it, then from whose point of view would the tension at your end be simultaneous with the motion at the other end? An observer halfway along? Then from your point of view it would happen a year after you tugged.  Whereas, if your mate at the other end tugged back as soon as your signal arrived, you would find that his response would arrive before... what?

Your string would be working by laws totally at variance with the rest of the universe, and all sorts of things would become meaningless. One thing for sure is that such a string could not be made of matter, because matter transmits forces by electrodynamic interaction, ie by photons, which means speed of light at most, and limited rigidity.

Before tonight (Pacific Coastal Time) you will have caused the number of String Theories to double, as each existing theory neatly divides into two in an attempt to account for the differing opinions of your teacher and yourself.

However, this will cause no damage, as there is already an infinite number of string theories.

And, speaking as a pedant, I do assert that the term 'an infinite number' is singular and therefore requires 'is' and not 'are'.

Light inextensible strings are part of learning mechanics. They don't exist any more than "light beams" (i.e. a plank with no mass), frictionless pulleys or uniform beams. Likewise, you cannot ignore energy loss nor air resistance in the real world. I'm not sure where you are with "M1" (lower sixth??) but it won't be long before they tell you that gravity is a bit less than you've learnt so far, and that air actually does offer quite a lot of resistance.

Whatever you calculate, faster-than-light ain't gonna work.

If you'd like to make alittle more sense out of Jon-Richfield's erudite response - I recommend reading up on Einstein's Special Relativity :)