It depends on how good your ad carry is. Normally if they're good at freezing the lane, then it wont matter, since when you clear a wave, the next wave will already be there. Allowing them to keep farming. But if they're not that good at cs, then taking the turret may not be the best choice.

Learning how minion waves push and ways to alter their pushing is a great skill to have, one that many don't.

I've tried to get my ADCs to freeze lane, but mostly they kept pushing and didn't listen to me at all :-/ The ADCs who are good enough to understand that strategy and when to use it don't usually have their towers taken.

kind of depends. if i'm laning against an pantheon/leona kill lane bot, they will keep pushing the lane and destroy my farm. i can't freeze the lane against them effectively especially when playing a passive farmer like ashe and varus

after all, their best strategy IS to keep you from getting to late game.

early tower is good if you've already gotten fed and can roam, but other than that yeah, it will hurt your farm, and levels

WTF?

Why dont stay at your lane instead and farm the enemy champs all the time instead?

This is the most wrong post of all time.

It is always correct to kill a tower, even if it is 3 minutes into a game.

I agree with this guy. I think gank is much important than farming. After you destroy the first tower, it means laning phase is over. It doesn't matter it's 10 min, 5 min, or even 3 min. When the laning phase is over, you start to roam and gank the other team.

By destroy that tower, you will have more chance to land more successful gank.

I disagree strongly with this. By the time you would have downed a turret on bot, you'll have enough gold to make you a threat, which makes roaming possible. You can do some serious damage roaming early- enough that it's almost impossible for them to claw back.

here's what will happen:

at 3 minutes into the game, there will have been 3 waves of minions (starting to 1:30). if you're really really good at CS, you might get 15-16 out of those 18 minions. that's 300 gold.

the tower gives you 150 gold for a total of 450 gold.

what are you going to gank with at 450 gold? you're the AD carry. you need items. with 450 gold you might as well be starting out at level 1. roam mid? that's a sure way to get yourself killed faster than you're going to be killing your opponent. stay in lane? if i'm the opposing AD, i'd be smart and freeze the lane much closer to my second tower. you're much more open to ganks from there.

in the meantime, your enemy ad is free farming near their second tower.

i don't think it's a good strategy to follow.