"While I understand the original idea was yours, I need you to understand that the prize we won together. […] That exhibition booth […] is as much mine as it is yours."
And of course either of you can choose to leave the team unilaterally, but on a 50/50 team, it seems odd that one person can "fire" the other person and take all the benefits (minus one ticket) that the team won together. If we formed a 50/50 team, and a VC gave us a bunch of funding, and I told you I was firing you and giving you some of the VC money, you would be pretty miffed.
If there's a booth to demonstrate things, then your statement here seems odd:
"The tickets being offered were exactly what he would have gotten as a team member.."
because there's more to the benefits of winning than a ticket to a conference or whatever. Additionally, you paint his email as harassment, but I really don't see it:
https://cdn-images-1.medium.com/max/2000/1*DQAH9nLoO8yC4rwtK...
I won't continue from there as hopefully you get the idea. And I'm not blaming you, but it really does not seem like harassment, despite the narrative you're painting. It makes me think you have some angle here, but someone shouldn't be "fired" and told to leave a project that they had a 50/50 stake in because you thought they were a little gruff.