Zookeeper requires at least 3 servers because of how it elects a new Activemq Master. Zookeeper requires a majority (n/2+1) to elect a new master. If it does not have that majority, no master will be selected and the system will fail. This is the same reason for why you use an odd number of Zookeepers servers. (EG. 3 servers gives you the same failure rate as 4 because of majority, can still only lose 1 server.)
For Activemq, the necessity of at least 3 servers is derived from how the messages are synced, and the fact that when a new master is elected, it requires atleast a quorum of nodes (N/2+1) to be able to identify the latest updates. ActiveMQ will sync messages with 1 slave, and then respond with an OK. It will then sync asynchronously with all other slaves. If a quorum is not present when a node fails, then Zookeeper has no way to distinguish which node is the most currently updated. This is what happens when you have only 2 nodes originally, so at least 3 is recommended.
From ActiveMQ site, under How it Works:
All messaging operations which require a sync to disk will wait for the update to be replicated to a quorum of the nodes before completing. So if you configure the store with replicas="3" then the quorum size is (3/2+1)=2. The master will store the update locally and wait for 1 other slave to store the update before reporting success. Another way to think about it is that store will do synchronous replication to a quorum of the replication nodes and asynchronous replication replication to any additional nodes.
When a new master is elected, you also need at least a quorum of nodes online to be able to find a node with the lastest updates. The node with the lastest updates will become the new master. Therefore, it's recommend that you run with at least 3 replica nodes so that you can take one down without suffering a service outage.