If you're not going to tolerate partitions, what does it mean to be available?

It means you're not running a partitioned and distributed system, but a regular non-partitioned system.

Yes I know distributed cloud object-graph databases on selective-persist elastic firesprout-nodes are very popular and trendy these days, but lots of people just run regular, old-fashioned unpartitioned databases, like pgsql/mysql and they work just fine.

I know. Like whoah, eh?