In a case study I read it showed that both water and air are counter current. The only reason I can think of for doing this is that you are trying to minimize the airflow rate (e.g. post-stripping air treatment is required). Is (are) there another reason(s) for the total counter current flow?
In the case study, they wanted an effective 12-stage stripper, so that is why the air is piped from the “follow stripper” into the “lead stripper." A more typical way to set up two strippers in series is to use a blower on each, which provides higher overall removal than the configuration used in that case study because both strippers have fresh air coming into the bottom stage.