Touching the magnesium metal can actually contaminate it and bring with it impurities which may not be removed by heating. So this leads to error in weighing.
There are two reasons not to touch the crucible tong with bare hands:
1. The crucible tong is used during firing so it is extremely hot and may burn your hands
2. Any impurities in your hand may contaminate the tong hence leading to error just like the case for the magnesium metal