Why does a blocking 1/1 creature with double strike kill a 3/2 creature?
Here's how the combat actually goes:

First strike damage: Attacker marks one damage (they are still 3/2, but with 1 damage marked), Blocker is at 1/1 with no damage marked.
Normal strike damage: The two creatures exchange damage simultaneously. The attacker marks another damage (still at 3/2 but with two damage), and the Blocker is a 1/1, but with 3 damage marked.
State-based actions are checked. Both attacker and blocker have at least as much damage marked than they have toughness, so both die.

(Technically state-based actions are checked after first strike damage, because they are checked when player priority changes, but there are no actions to check.)
Really, the only difference is that the damage doesn't take effect immediately, so read up on state-based actions to learn more.