To pull out is to withdraw from a deal, a race or an agreement. You were in it and now you are not.
It takes of. Business and sport use it constantly, so a sponsor pulling out of a deal is a headline. There is a driving sense too, since pulling out of a junction means joining a road, and it is the manoeuvre that causes the most accidents. Troops pull out of a country, which is the military sense, and a pull-out is a removable section of a magazine.
Middle English
pullen oute
English, today
pull out
From Middle English pullen oute.
Etymology from Wiktionary, CC BY-SA