In most normal scenarios, you would be uploading activity to Garmin Connect via the ANT Agent or Garmin Express. If all you are trying to do is to get activities off of your device and into Garmin Connect, this post should help.
If you are wanting to manually upload a tcx/gpx/fit file, then either the functionality is intended to be added and just isn't there yet, or there is no intention of adding it. Rumors indicate that the less appealing of the two is the direction things are heading.
Same issue here. Garmin Express only wants to push a new 5.1GB map to my device (a map I don't need), I haven't found a way to simply upload activities. The old-style interface was much better, but now it seems either non-responsive or erratic :(
Thanks for the clarification @Travis.vitek - this is a poor turn of events for linux users, since there is no Garmin Express for linux. Once again, I am astonished at the functionality that Garmin continues to REMOVE from Garmin connect.