She was supposed to follow in Bella's footsteps, follow in the footsteps of all those before her, and set a good example for Cissy when she came to school. That was her job. So, Andromeda Black became a part of Slytherin, because she hardly had a choice in the matter, anyway. She was setting the perfect path for Cissy to follow, just as she was supposed to be.
Sirius, however, well, he was everything Blacks weren't supposed to be: reckless and rebellious and very Gryffindor. But she just might have clapped under the table when he ended up breaking tradition...
AN: Happy birthday, Harry. Anyway, I was always under the impression while reading the books that Andromeda was a Slytherin. I checked online (which, sure, isn't the most reliable source), and it agreed with me. So, yes, I'm aware that some people view her as a different House. If it says otherwise in the books, of course, go ahead and tell me. But for now I'll go on my own impression and the semi-reliable websites I've gotten this information from. Thanks for reading.