Well, putting aside for the moment the argument over whether or not this should be allowed, it's definitely not a bug.
Sites have specific "migration paths", which are a reflection of which off-topic questions actually get asked. Stack Overflow used to collect a lot of tech-support questions and some sysadmin questions, which now belong on Super User and Server Fault respectively. New migration paths, like DBA, got added partly because those fledgling sites really needed the questions, and it was too convenient to just keep asking on the (much) higher-traffic site.
If we see any questions about pets here, they must be extremely rare. What you're calling biology questions (I assume you mean the obnoxious "prove to me that 2 hours of bacterial growth is really dangerous, otherwise I'm going to eat this rotting steak" questions) aren't really biology questions in the sense that they would be accepted on the Biology Q&A. The science Stack Exchanges are intended for academics and researchers and don't want to be flooded with random "popular mechanics" nonsense.
The idea is, migration is only allowed when two sites are clearly overlapping and one tends to attract a large number of questions that should go on the other. And even then, migration is only allowed to continue when the originating community has a good track record for migrating questions that are on-topic for the destination site.
I have serious doubts that most of the community here is familiar enough with the rules on Biology, Skeptics, Brewing, etc. to responsibly choose which questions should be migrated there vs. which should simply be closed. Migration doesn't mean "we think this might be more on topic on your site", it means "somebody posted this on site X by mistake, it definitely belongs on site Y instead." It's a strong statement that very few of us are really qualified to make.
Even the moderators can't just migrate to other sites willy-nilly. I have no idea what the specific rules are - probably something to do with time or votes - but we only see the "belongs on another site" option for a small number of questions. So flagging for moderator attention isn't necessarily going to help either. Just close them.
Generally speaking, off-topic questions also tend to be poor questions anyway and could do with a rewrite rather than a migration. In these cases the low quality trumps the low relevance. So that further narrows down the set of useful migrations - we should only be migrating questions that are definitely on-topic on the destination site and reasonably clear/succinct enough that they wouldn't need to be edited (much) on the destination site.
Given all this, how often would we really need to migrate questions to other sites, even if we could?