Why does my meat never thaw in the fridge?
The difference between cold and frozen where a refrigerator is concerned is actually only a few Kelvin (or "degrees"). 

The standard refrigerator will have warmer and colder zones, typically the top shelf being warmer, the bottom shelf above the veggie drawer cooler. Likewise the back is usually cooler than the front. The temperature you set it to is an  average value. (Check your manual for your model.) In mine, anything on the back of the lowest shelf can, on occasion, be slightly frozen, but I have set it to 4 C.

Also, thermostats in kitchen appliences can easily be off by a few degrees. We have discussed this for ovens here on the site often enough, the same is true for fridges and freezers. A calibrated thermometer can tell you more.

So once you have made sure that your meat actually can thaw by putting it on the top shelf and adjusting the temperature setting, it's all about patience. The time it takes for a piece of meat varies greatly and for a big "lump" like a whole roast, defrosting overnight won't happen. Prominent example: Around Thanksgiving the defrosting times for turkey are discussed all over the web and plenty of anecdotes told about cooks forgetting that it may take days for a large bird...

That's one of the reasons why it's generally recommended to freeze food in smaller, especially flatter packages where possible (e.g. steak or chicken breasts side by side, not on top of each other): It freezes faster (-> food safety) and thaws faster (-> convenience).