>>89941763>>89942220推す doesn't mean push, it's 押す that means to push. They're just homophones.
推す literally just means to support or be a fan of, it's just a coincidence that english also has the term "push for" when it comes to supporting something or being a fan of something.
hell 推 as a lone kanji carries the meanings of conjecture, infer, or guess.
Just like what you see in 推薦 recommendation or 推定 assumption