Saved by the Brit - Shabbat 132a

"How do we know that the saving of life supersedes the Sabbath? R. Eleazar b. 'Azariah said: If circumcision, which is [performed on but] one of the limbs of man, supersedes the Sabbath, the saving of life, a minori, must supersede the Sabbath"

The argument that saving a life supersedes Shabbat is not unique to this sugya - however, the inference that saving a life is acceptable from the fact that circumcision is acceptable is fascinating. The logic here implies a quantitative interpretation of saving a life - surely we are intended to infer that circumcision thus 'saves' in some way, in order for it to be used to prove pikuach nefesh. If so, how does circumcision 'save' per se? Is it that it preserves the covenant? Or perhaps that it 'saves' the child from being excluded from the Jewish community? Whether one of these or another, I think the insistence on circumcision as a type of salvation begs to be interpreted, and might shed new light on a ritual that troubles many for what they see as harming a new life rather than saving one.