I don't think there is anything especially unprofessional about communicating via instant messaging. Email is a naturally asynchronous communication platform, and sometimes you need a synchronous method to contact people.
In my research group, we use a specific professional instant messaging application - Slack. I did this because I feel it's important to keep work and private life separate, but still need a way of communication synchronously with my team. Students/postdocs may exit/silence the app when they feel they are not on "work time". Your institution may also have such a system - Microsoft Teams, Google for Education's Chat and Facebook Workplace all offer similar functionality depending on which your university runs its IT systems on.
I should also point out that the opposite problem is also true. My students definitely think it's a bit weird that I refuse to be on their WhatsApp group.
That said, if instant messaging makes you uncomfortable, you should tell your supervisor this. There is no reason to lie about the reason - you shouldn't even need to offer a reason. You can just say "I'd rather be contacted by email unless it's a real emergency, if that's okay.".
This answer was written before it was clear that the OP was an undergraduate in a class, not a post-graduate communicating with their supervisor.
I do think it is a bit weird for a professor to be communicating, one on one with undergraduates in their classes via IM.
There are situations where some sort of chat system might still be a good way to communicate with students (I use slack in a large, long-term, practically based course I teach), but I do think personal IM is best avoided with undergradutes.
I don't think this changes the course of action, which would be to contact the prof and say you'd rather the contacted via a different means (see @henning's answer).