There shouldn't be a comma in this sentence: I like cats because they are furry and they feel comfortable. You'd only use a comma if you started with because: Because they are furry and they feel comfortable, I like cats.

I like cats, because their furr feels so fluffy and they are comforting.

‘Feeling comfortable’ and ‘making you feel comfortable’ are completely different things, but neither seem to apply. Maybe you mean: I like cats. Petting their soft fur makes me feel good. An example of ‘feeling comfortable’: I felt comfortable when I walked into their house. They had a pet cat running around, just like I do.

When your cat feels comfortable, it will lie down and go to sleep. If you and your cat are together and your cat feels comfortable, it will purr for you.