This is not a fight. There are no sides. There is no contest to be won. Both of you can only lose if you push her away...
Don't teach your kid what to (not) think or believe. Help her understand how to think and research.
Let her draw her own conclusions. Yes, they may be different from your conclusions.
Ask questions. Not to shame, be to understand what she thinks and why.
Ask questions. Not to destroy and attack, but to provoke her to actually think.
Oh btw...if your daughter actually said you shouldn't be pushy (did she really say so?), you were pushy. Even if you were not. Try to figure out why she feels that way. It can help you improve your relationship with her.