Here's a simple data setup, along with the query at the bottom you need to solve your problem. Essentially, you want to query for situations where a relationship doesn't exist. The syntax here is for neo4j 2.0, so the answer would be slightly different for older versions.
neo4j-sh (?)$ create (t:Teacher {name:"Bob"})-[r:TEACHES]->(s:Student {name:"Mary"});
+-------------------+
| No data returned. |
+-------------------+
Nodes created: 2
Relationships created: 1
Properties set: 2
Labels added: 2
19 ms
neo4j-sh (?)$ create (t:Teacher {name:"Mark"});
+-------------------+
| No data returned. |
+-------------------+
Nodes created: 1
Properties set: 1
Labels added: 1
5 ms
neo4j-sh (?)$ MATCH (s:Student) WHERE NOT (s)<-[:TEACHES]-(:Teacher) RETURN s