Why is there no 1v1 map?

there should be one so champions can go one on one with out anyone comeng in the game wasting time

Then suddenly, vs

That's true, Zed would be in a lot of trouble in that match up.

As others have said, Howling Abyss was the map, game mode was called Snowdown Showdown or something like. It was either 1v1 or 2v2. Win conditions were 100 cs, first blood (2 kills if 2v2) or turret destruction.

As to why they took it down, it was a feature game mode. Also, towards the mid/end of the game modes life, a very low percentage of players were actually playing it. Personally I liked it because I got to dumpster kids in lane. 8)

In the mean time, setting up custom games with your friends is the only way to go.