The only time you really should be last-hitting is when your enemy clearly has no means of killing minions while you're laning. Some examples of this would be if you're up against two melee champions and you have two ranged. If you keep them off of the wave then stand between them and the wave combat and just deny them EXP and gold then thats a good time to last-hit. Also if your in a 2v1 lane (you being the 2) you should last hit until you can force the solo to recall then push. A great example of someone you should be last hitting against is Tryndamere. He is worthless early game in the waves so if you can keep him out of the combat by griefing him then you can last hit him out of a lot of gold and exp if you do it properly.
I don't know why these people are saying not to push and last hit. If you have the power and you're not putting the enemy at a disadtvantage by last-hitting then push. An enemy behind towers is a lot easier to deal with then an enemy in the brush or MIA. Keep your enemy pushed back to their tower and their tower will steal their gold. Towers mean everything in LoL, not worth your life, but taking enemy towers greatly decrease their map awareness and their map control.
Edit: Also I wasn't implying that if a minion is low on health you shouldn't focus it to get gold, I was implying you shouldnt JUST last hit minions except in these cases.If a minion clearly has low health then kill it, but that is just common sense.