you have soem what explaiend the answer, you are right about you calculations too, say we always prefer R_th to be as lower as possible to get more power out by decreasing R_L, since R_th is there it makes voltage drop so that at a point your drawn power will start to decrease with lowering R_L.
you work with some practical values, say your source is 5V, R_th= 2, now you connect a 1 ohm to the source and calculate the power, then 3 ohms, keep on approaching until 2, the maximum value would be at 2. as i remember this method is called successive approximation...