This is the 8529th most frequent Japanese word.
押し付け
"押し付け" means "imposition" or "forcing something on someone."
"押し付けた" is used here to indicate that someone forcefully enforced their opinion onto others.
彼は自分の意見を押し付けた。
He imposed his opinion on others.
"押し付けて" is used to describe the physical action of pressing something firmly against a surface.
重い荷物を棚に押し付けて置いた。
I pressed the heavy bag onto the shelf and placed it.
"押し付けないで" here expresses the act of forcing someone to take responsibility without consent.