He explains his choice in lines 8-9 on p. 364 of the paper:
"This metric has the curvature $-4$ for it is obtained from the hyperbolic metric by the transformation $w'=w^{1/2}$ ."
Remarks. By more sophisticated choices of metrics later authors, M. Bonk (MR0979048) and Chen and Gautheier (MR1428103) were able to improve Ahlfors's estimate of the Bloch constant.