Hey fakrampe,
If you delete an email on your Mac first, does it delete from the iPhone? If the sync seems to be broken both ways, try restarting both devices and test the issue again.
If the issue persists with only the iPhone, try removing the account, and the adding it back again. Most email accounts store all the emails via a web server, however it may be worth confirming with your email provider that their accounts work in that manner to ensure there is no data loss.
"Log out of or remove email accounts
- Go to Settings > Mail > Accounts.
- Tap the email account you want to remove, then do one of the following:
- If you’re removing an iCloud email account: Tap iCloud, tap iCloud Mail, then turn off “Use on this iPhone.”
- If you’re removing another email account: Turn off Mail.
- Note: To remove the email account from all apps on your iPhone, tap Delete Account."
If you notice they still don't sync, contact Apple Support directly for additional assistance.
Cheers!