Actually, having it in the middle does nothing.
Because the slab will usually have a load on it from the top, that places the top of the slab in compression and the bottom of the slab in tension. The centre will be neutral. The steel needs to be nearer the point of tension as this is the weak point of concrete. Put the mesh nearer the bottom of the slab. In saying that, it needs 1 1/2 inches of cover.
Slabs on grade work differently than suspended floors. For a typical garage floor where cars are driven: (Industrial floors or floors with very heavy industrial loads behave differently and have a different set of guidelines/needs.)
Slabs on grade
need to have the reinforcement in the middle. This acts to keep shrinkage and cracking in check. The solid ground under the slab causes the structure to behave differently and
tension reinforcement is not needed. (If you think of the floor as a composite beam, the ground underneath the concrete is part of that system and the compression strength of the concrete is the thing that is needed at the top levels.) Good reinforcement in the middle of the floor will keep it looking nice for a very long time. (This is a good technical article on the specifics of all this:
http://www.wirereinforcementinstitute.org/pages/pubs/pdf/TF 705-R-03.pdf but going through all these calculations is probably overkill for a garage.)
That being said... putting the reinforcement in the middle is not an easy thing to do. It must be supported from the bottom and suspended in the middle. Shoddy contractor work here is common. You'll see a lot of contractors just laying mesh on the ground or laying it down at half-pour. In these cases, the mesh ends up sinking to the very bottom where it does absolutely nothing.
Its also possible to overdo the steel. If too much reinforcing steel is installed, then the concrete will be weaker in compression. Its important to follow local code regulations and not go beyond. For the strongest system, you want just enough reinforcing to control cracking and nothing more.