Well, it might seem weird to you, but unfortunately it's not.

Private company shares aren't furniture. They aren't physical property and they don't come with traditional resale rights.

In buying those shares you signed a contract that came with stipulations. One of those stipulations is that you cannot transfer ownership to anyone else. It's perfectly normal and very common.

I just hope you're not realizing this for the first time, now, after you already laid out the capital to exercise those options.