Simple
Transference
You see the other in the same way as you believed
your parent to have been.
You see the other as being like what you WISH your parent COULD have been like.
You see the OTHER AS YOU were as a child and you act like your parent
did.
You see the other as you were as a child and you act like you WISHED
your parent could have acted.
Note:
This transference is a bit different than how it is applied to
psychoanyalytic therapy. Not
talking about a neutral or "blank screen" therapist onto which the
patient projects and recreates patterns from childhood. The person you describe may indeed be something like the
parent. Nevertheless,
the "transference" may still be evident in the fact that you have
chosen someone with whom to recreate an old parental relationship, in how strong
the person reacts to that characteristic of the other person, or in the whole
variety of ways the person thinks, feels, and behaves in reaction to that
characteristic in the person you wrote about.