With my company, the PF will tell the PNF to request push and start, if the PNF does not feel it is safe or appropriate (could be capt or FO) then he will say so. Same with taxi, PF will direct the PNF to call for taxi after the after start flows and checklist. If it is not safe either pilot or ATC can say it is not safe.
The FO taxiing may take some getting used to for you as well.