It’s certainly possible in the sense that anything like that is possible when there are humans involved!
Assuming that you are working with a competent therapist, I would put my money on it’s your stuff talking in this situation. You are having some challenging feelings around your plans to become a therapist and projecting those onto your therapist. That is a very normal thing to do in therapy by the way, so no judgment here!
My recommendation is that you bring this up with your therapist. Tell him what you are observing and experiencing and how you are feeling. Your therapist should know to not take this personally and instead help you explore the perceptions and feelings that are playing into this for you. This sounds like future breakthrough material for you, so I hope you go for it, but definitely pay attention to your own comfort level and work at the pace that works for you.
On a personal note for a time I was thinking I wanted to pursue a second career as a therapist and discussed this ambition with my own therapist. He was very supportive, and told me that I would be very good at it and had the right temperament for it. He also gave me some helpful information about the process and where both the degree and continuing education fit into it. I ended up discerning with his help that this isn’t quite the direction for me but talking about it and considering the possibilities were very positive experiences for me, including the conversations that took place in sessions.