Why does I2C look like this?
The ICs internally use open drain/collector drivers to actively pull the signal low so you see "fast" fall times.  In contrast, when the drivers are off the line is pulled high through a pull-up resister and consequently you have a longer RC time, and a slower rise.

You don't say what kind of the design this is.  Is it a commercial device or something you've soldered up or perhaps built on a breadboard.  Depending on those things you may want to check the connections and size of resisters being used.  It might also be that the ICs you're using require that you enable pull-ups.