Losing is all I seem to be able to do. I do nothing but training mode for weeks at a time, then go online and get destroyed by every possible team combination. I can barely get any moves off, I don't feel like I'm learning anything and am generally not having any fun. I don't understand how every player I come across is an expert.
Just whining.
Well I have no idea why exactly you are losing but one tip that could help is learning how to tag out effectively. An average team should have around 2000 health but that really isn't a lot considering how easy it is to get damage in, so tagging out and getting back that recoverable health can save you by hundreds of points of potential damage. Instead of trying to use meter to make a long combo and do more damage, you should be using it to make a safe tag-in to last longer in the match. The worst case scenario of not using a tag-in would be your first character dying before you even try tagging in because you were too greedy or didn't want to risk your second character losing some life. Essentially, you are only using 50% of your maximum health and that could be a significant factor in your losses.
Also if you don't want to be frustrated online, try player matches. This game is full of gimmicky shit and some players will abuse it just to get ranked points. If you find someone of your skill level in a player lobby, just keep on going at it until you learn.