France wanted it to go through the Bering Strait or the Azores, and made the argument that the SI meter (introduced nearly 100 years before) was a truly neutral measure, being based on one ten millionth of the distance from the equator to the North Pole. Other delegates answered that its is still a French system, because it was France that took the measurement and introduced French error into it.
Ultimately practical concerns won out, as 70% of the world's shipping and charts were already using Greenwich as the meridian, and for any other place to truly be a meridian there would need to be an observatory there with telegraph links to the rest of the world.
Another gem is the part where the Spanish delegate expressed that he had been authorized to vote for Greenwich as the meridian, but was doing so in the hope that England and the United States will accept the metric system. The president replies that this is outside the scope of the conference, to which the Spanish delegate replies that they know this, and anyway protocol doesn't allow them to vote on "hopes" anyway, but he just needed to say it.
Although Greenwich was chosen, France was a holdout and didn't adopt it until 1911, and even then did not call it "Greenwich Time", but rather "Paris Mean Time retarded by nine minutes and 21 seconds." This was their official designation until they adopted UTC. The UK on the other hand still calls their time GMT legally, even though they are actually using UTC now, which is not precisely the same as GMT!
The proceedings make for some entertaining and enlightening reading: http://www.gutenberg.org/files/17759/17759-h/17759-h.htm