Is there such a term for a motivation that makes someone avert from being a particular way?

No, there is the word 'phobic' which means 'fear' as in 'fear of' which makes people react negatively towards something and you get it on the ends of all sorts of words, such as hydrophobic (fear of water - will not go near or in water) or claustrophobic (fear of small spaces - will not go into a cupboard otherwise they will get distressed). People may wish to say someone is a reactionary, meaning that they react violently in one particular way because of their reactions to something else, but this usually has political connotations, such as a political reactionary will often be quite militant and want communism and not democracy. Depends how you use words in their context. You could use something metaphorically, and then it would be OK.