I think I know the problem you're having, I had it too. If you try to assign the task from the web app you get a message that says "that person is using the old version of the app." But you're both using the new mobile apps right?!

Turns out both you and your contact need to log in to the new web app at least once.

* Log in at https://www.rememberthemilk.com
* Upon logging in, you should be prompted to swap to the new web app or click "New stuff!" at the top right.

Should be able to give tasks after that.