"This cat is my boss, not my pet!"
Translation:Diese Katze ist mein Chef, nicht mein Haustier!
Well you can think of it like the gendered English words:
waiter - waitress / actor - actress / host - hostess / lion - lioness / bull - cow / drake - duck / warlock - witch
In English, when we don't know the gender or don't care, then we just use the a specific version that is considered neutral. Typically, it's the male version, but not always.
We can say She is an actor but we can't say He is an actress. He is a cow but not She is a bull. She is a waiter but not He is a waitress. He is a duck but not She is a drake.
In German, it's similar.
I put geschäftsführer instead of chef, would that be ok in reality?
I'd find it odd to talk about mein Geschäftsführer because a Geschäftsführer is someone who leads a company, and I'm not a company. In order words, a Geschäftsführer "belongs" to a company, not to a person.
Not exactly. Katze is feminine in the grammar sense. However, a cat, in general, whether male or female can be referred to as (die) Katze. So you could say either “Diese Katze ist mein Chef” or “Diese Katze ist meine Chefin”. The default, when gender is unspecified/unimportant, is to use the male form (Chef). If you really wanted to emphasize that it was a male cat, you could perhaps say “Dieser Kater ist mein Chef”. Note that Kater is more often used to refer to a hangover than a male cat.