"You made me do it” and “It's all your fault" are two favorite sayings of blame shifters and guilt trippers. Except no one makes you do anything nor do you make anyone do anything. When you or I do something wrong, our sin does not transfer to another nor does their sin transfer to us. When anyone chooses to do something wrong it is by choice - their choice.
The Bible is very clear on that teaching, even in the OT law. When Moses was reviewing the Law with Israel before they entered The Promised Land he included a discussion of this principle in the middle of a lengthy discussion of applying equal justice under law (Deuteronomy 24). In verse 16 we're told that no one should bear another's punishment. The father shouldn't bear the son's and vice versa; concluding with the idea that each person should be punished for "his own sin".
So why do we do it? Well, blame shifting goes all the way back to the Garden of Eden when Adam blamed Eve, and, by extension, God, for his own sin (Genesis 3:12). One of the problems with sin is that none of us wants to accept responsibility for our own. Oh, we may admit it, but then excuse it by blaming..., well - you. One of the blessings of the Gospel is that Jesus broke the chain of blame shifting and voluntarily took the punishment for our sin (Romans 5:6). We just have to admit that it's our fault and stop sinning.