There are several reasons for that.
- Towers are particularly strong, early game, in League of Legends
Even if you want to push, you won't actually be able to destroy a tower during the early game, and it can kill you quite fast. So while it seems intuitive to push when you are at advantage, it's a strong limit preventing you to push further, even if the lane goes good for you. This leads to the next point...
When you push, the distance to your tower (and so, your safe place) is increasing, while it's decreasing for the enemy. As such, it will be complicated to actually damage them and even more to kill them. And at the same time, you are more exposed and have a greater distance to walk if things go wrong.
You might not have this situation in early levels, but the current metagame is such that you normally have one player in each team roaming in the jungle, and ganking lanes.
As such, by pushing your lane, you expose yourself to the enemy jungler while the enemy is protected from your own jungler, safe at their tower.
In the current metagame (at least for western countries, it's a bit different when you see korean players, for example), there is a phase of heavy farming at the beginning of the game. To optimize this farm, you need to be safe, and have the minions accessible.
That's why pushing too hard, and killing the enemy tower too early can be a problem. In early game, the enemy tower helps you with farming, because it limits the distance where your creeps are going. Since there is no denying in LoL, it's actually the only way to have a sure limit for them.
Without the tower, your farm area is easily pushed farther in the enemy territory, which doubles the risks from the two previous points.
The only advantage I can think of pushing your lane is to force the enemy at their tower. Farming under the tower is complicated, as the tower will take a lot of the last hits on creeps. By pushing the enemy under their tower, you can deny them a fair amount of gold.
But it remains risky, and it will be enough for their jungler (or mid-laner) to come to your lane, to force you to retreat (unless you really have such advantage that you can take them 1 vs 2 or 2 vs 3, depending on the lane). So even if it looks like you are at an advantage, you might actually be offering them an easy kill or two. So careful with that, as the matchmaking level increases.