Question

Why half deflection method is only used for calculation of resistance of galvanometer?

Answer 1

according to my point of view half deflection method   is the best for finding resistance of galvanometer due to it gives me simpler expression.
              $R_G=\frac{Rr}{R-r}$
where, $R_G$ is the resistance of galvanometer.
               R is the high resistance in series with galvanometer.
               r is the low resistance in parallel with galvanometer.
From above it is clear that,
              R >>> r , so, ( R - r) ≈ R 
now, $R_G=\frac{Rr}{R}=r$
             hence, we have to find the resistance of galvanometer, you can  say that it is approximately equal to low resistance in parallel with galvanometer.

    for understanding, Let one example :
                          R = 10,000 Ω
                           r = 50 Ω
now, $R_G = \frac{10000\times50}{10000-50}$
                       = 50.25 Ω ≈ 50Ω 
 

Answer 2

When we are given unknown resistance to find its value. The method that comes to our mind first is by Ohm's Law.
By measuring V and I and then R=V/I

But this method gives some inaccuracy because ideal ammeter must posses zero resistance and voltmeter with infinite resistance.
But no devices are idea.

Hence we prefer to use half deflection method to measure the unknown resistance value..

Expression used :
 Rg=Rr/R-r

where Rg is the resistance of galvanometer 
R is the high resistance in series with galvanometer
r is the low resistance in parallel with galvanometer.
R>>r, so (R-r)equals R

Now, Rg=Rr/R=r which equals to the low resistance in parallel in galvanometer.