The reasons I don't like database triggers:
1.) They are very difficult to debug
2.) They are a type of "magic" within a system. "Magic" is when something happens when I run code that I don't see in the code.
3.) They are not intuitive.
I find that database triggers get used in an organization when one or more of these things happen:
1.) A DBA has been tasked with writing application code
2.) The code is more difficult to change than it is to debug a database trigger
3.) The deployment process for code is significantly longer than the deployment process for SQL changes