It may seem misleading to think that a self-hosted email would be more secure than one provided by a large, credible institution. Unfortunately, the concern here is not necessarily security - it's privacy.
My institutional email from Brown is, under the surface, an email inbox provided by Google. Google's privacy policy documents many aggressive, harmful practices. Not least is the following quote taken directly from it:
We also collect the content you create, upload, or receive from others when using our services. This includes things like email you write and receive, photos and videos you save, docs and spreadsheets you create, and comments you make on YouTube videos.
You might ask why Google has any interest in our conversations. The main interest Google has is revenue - they will use every character in those emails for their own profits via advertising, profiling, training of large language models, or whatever else they deem necessary. Of course, there are other places that our conversations can go at Google's will.
It is for the above reasons that I urge you to use my personal email and use GPG to keep our communications between us.