Reasons email is bad

• Spam is rampant
• Running your own server is a major pain
• If you aren't on gmail, gmail assumes you're sending spam
• Everyone else is on gmail
• Attachment limits are obnoxious and arbitrary
• Nobody knows how to validate addresses
• Configuring TLS, SPF, DKIM, submission, etc. is confusing
• Random RBLs will blacklist you based on superstitions, and admins of other email servers will trust RBLs without question
• Many useful protocol features have been completely forgotten in the quest to eliminate all spam (retry, MX forwarding, etc.)
• Random things don't understand MIME encoding for some damn reason
• Many clients don't know how to handle HTML correctly and/or safely

Reasons email is good

• Technically it's decentralized
• You can self-host it for not a lot of money
• There's a wide array of interoperable clients that work without a lot of proprietary nonsense
• Message headers are very extensible and useful for all sorts of unexpected things
• MIME encoding can do some really useful stuff
• It's private by default
• It's federated by default
• Spam filters have gotten pretty good for the most part
• You can have your own domain name and move it between different providers rather than being tied to your ISP and/or Google

Reasons email is better than the things people try to replace it with

• You can keep control of your notifications via message filtering, etc.
• Message filtering can be incredibly flexible
• Pretty good search (especially in modern clients, with client-side caching)
• Threaded messages can provide better context for a conversation and also allow people to self-edit and take more time to think about what they're going to say
• Writing "bots" and email-based APIs in general is much, much easier
• Signatures can add a lot of personality and useful information
• A broad choice of clients that satisfy varying accessibility needs without randomly A/B testing your experience

All in all, email is pretty okay.

(That said, if you want to run your own setup, Mailgun makes things a lot easier. Not sponsored, I just like them.)