What becomes wrong when one envisions a multiverse is the concept that there is an 'individual'. In fact, there is an infinite number of people exactly like you, who make exactly the same decisions, and live the same lives, only at one point they sneezed a fraction of a second earlier than you did, or moved one nanometer further to the right, or whatever.
But you still have free will. If one of your counterparts moves right, you can still move right, too. But an infinite number of people also go right, and another infinite number go left. All the infinities are just really hard to deal with.
As an aside, there's the story of the infinite hotel. Imagine an hotel with an infinite number of rooms. Say it's full, it has an infinite number of occupants, filling all the rooms. But you come in, and rent a room for the night. How will you fit? Well, the clerk, experienced in such matters, just asks all the other tenants to move up one room; those in room 1 move to room 2, and so on. Now there's an empty room, but no-one has left! In fact, you can use this method to vacate an infinite number of rooms! Just an example of the intractability of infinities.