To insist on and carry something through; to force one's will or plan ahead despite opposition or obstacles.
彼は反対意見にも関わらず、その法案を押し通した。
He pushed the bill through despite opposing opinions.
会議で自分の案を押し通すことは得策ではない。
Forcing your proposal through at a meeting is not a good idea.
彼女は計画を最後まで押し通す意志がある。
She has the determination to carry the plan through to the end.