I've attempting something similar before so here's a non-exhaustive list of problems from the top of my head:
1. Getting to send email, at all: lots of hosting providers blacklist outgoing port 25 TCP specifically to prevent random people getting their IPs put on a spam blacklist
2. Getting your IPs de-blacklisted: unless you get really lucky whatever IP you _start_ with has a good chance of already being on several blacklists, and some make it stupidly hard to get your IP off the list even if the ban was from 5 years ago by whoever had the IP back then
3. To even have a chance of your emails being deliverable you have to understand and configure reverse DNS, SPF, DKIM, DMARC (and probably a few other I've forgotten or which have been invented since I tried this)
4. Even after you get this far, major providers like gmail are likely to send your email straight to /dev/null because you're a new provider with no reputation
5. If (or more accurately when) somebody manages to abuse your service to send a ton of spam you'll get re-blacklisted and have to fix that all over again and implement/fix spam filters to stop people like this (this will probably happen several times as you constantly attempt to battle spammers)
6. You're going to want some sort of incoming spam filter, because people don't really like spam in their inbox, and most existing open source and/or free solutions are mediocre at best
7. If you use a weird TLD (i.e. not .com/.org/.net/similar) random online business will not allow your email or not send to you properly, and your customers will blame you despite you being able to do almost nothing about it
8. Even if you use a "standard" TLD to get past 7 some particularly bad actors will use a email domain _whitelist_, so only gmail and friends are allowed, and again your users will blame you