I think there are multiple layers behind why someone might find "they" inappropriate. I don't think they're necessarily all valid but I think they're understandable.
1) Gender is currently a political topic. The use of gender neutral pronouns is, rightly or wrongly, associated with holding certain political beliefs. People who do not hold these beliefs are likely to reject their use on that basis.
2) Gender is a matter of personal identity. A fairly common desire for people is to be "good" at the gender they identify as. A fundamental part of that is being recognised by others as that gender. Gender neutral pronouns refuse to provide that acknowledgement.
3) They can be unfamiliar. Ultimately pronouns are something that, until recently, most people never actively thought about. Some people will reactively reject them as it puts into question their understanding of the world.
1) Gender is currently a political topic. The use of gender neutral pronouns is, rightly or wrongly, associated with holding certain political beliefs. People who do not hold these beliefs are likely to reject their use on that basis.
2) Gender is a matter of personal identity. A fairly common desire for people is to be "good" at the gender they identify as. A fundamental part of that is being recognised by others as that gender. Gender neutral pronouns refuse to provide that acknowledgement.
3) They can be unfamiliar. Ultimately pronouns are something that, until recently, most people never actively thought about. Some people will reactively reject them as it puts into question their understanding of the world.