It sounds like you are misunderstanding the combat system. You do not need a 1 die result to hit one INF. Against 1 INF all of your results of six or less will go in the INF unit’s address. All you need are two results of 6 or less to destroy. Any result of 6 or less will force the INF to retreat.
If you have been playing that one INF only gets hit on a one there is the German difficulty. If you have say 2 INF and 2 ARM defending a hex the INF will take hits on results of 1 and 2 and 5 and 6 because of wrap around. The tanks get hit on 3 and 4.
Germany moves first and will be able to move into a vacant hex during phase three. Units off the reinforcement chart can be moved into those hexes as well if they are on a road. Tanks may blitz from the chart into them if they are “off road.”
http://www.axisandallies.org/forums/index.php?topic=8246.0 At the end I give an alternate explanation of the combat system.
Try the game where you don’t needs a 1 to kill 1 INF. That will change your perspective.