Attempt no. 2 at posting this, due to busy server.....
I fly a C172 from a long tarmac runway, and use the method of instructor 2 (except it's airspeed and not ground speed of course). A positive rotation gives the benefit that you can hold the a/c on the runway until the airspeed is well past the stall speed, although too enthusiastic a rotation could lift the nose too high and enter a stall, which is not advisable without airbags...
The POH will give the definitive speeds, based upon MTOW, although if the a/c is at or near MTOW I always add a few knots extra to the take off speed before rotating where the length of the runway is not an issue.
The instructor teaching method 1 may be trying to get you used to flying from short runways. Short-field technique (which of course differs depending upon a/c - always check the POH as FFF suggests) usually involves gradually increasing back pressure to get the a/c off the deck as early as possible. The downside is that when the a/c flies off the runway in this manner, it has only just reached flying speed. Therefore it is also very close to stall speed so care must be taken not to lift the nose too quickly and to allow the airspeed to increase before commencing a climb, otherwise those airbags will be needed again.
If you were using the soft-field technique you would probably try to unload the weight off the nosewheel as early as possible in the take off run to reduce drag from friction (wet grass, mud etc). Obviously not an issue from tarmac but if you are still learning, the instructor will try to familiarise you with different techniques for the conditions and the runway type/length. You won't always have the luxury of 1km or so of tarmac...