Auto increment is a no-no?

Hello. I must confess that I am rather new at this. During my courses, I was taught to place an auto increment as an id field in my tables, when in need to.

However, recently, I heard someone comment that this is to be completely avoided. But I do not understand why. Perhaps anon could point me in the right direction?

At work we had a very difficult time because the databases were modelled in an elegant relational way. Basically, the primary key to our most important table lost its semantical value (due to unpredictable circumstances). We had millions of records. Changing it was nearly impossible. We had to add an extra column and change the way hundreds of applications worked.

There's something SQL people have a hard time to understand: data changes.

Fuck you, data modelling faggots.