Deadlock error in INSERT statement

What PostgreSQL does here is covered in the documentation on Explicit Locking. The example in the "Deadlocks" section shows what you're probably doing. The part you may not have expected is that when you UPDATE something, that acquires a lock on that row that continues until the transaction involved ends. If you have multiple clients all doing updates of more than one thing at once, you'll inevitably end up with deadlocks unless you go out of your way to prevent them.

If you have multiple things that take out implicit locks like UPDATE, you should wrap the whole sequence in BEGIN/COMMIT transaction blocks, and make sure you're consistent about the order they acquire locks (even the implicit ones like what UPDATE grabs) at everywhere. If you need to update something in table A then table B, and one part of the app does A then B while the other does B then A, you're going to deadlock one day. Two UPDATEs against the same table are similarly destined to fail unless you can enforce some ordering of the two that's repeatable among clients. Sorting by primary key once you have the set of records to update and always grabbing the "lower" one first is a common strategy.

It's less likely your INSERTs are to blame here, those are much harder to get into a deadlocked situation, unless you violate a primary key as Ants already described.

What you don't want to do is try and duplicate locking in your app, which is going to turn into a giant scalability and reliability mess (and will likely still result in database deadlocks). If you can't work around this within the confines of the standard database locking methods, consider using either the advisory lock facility or explicit LOCK TABLE to enforce what you need instead. That will save you a world of painful