What are all the reasons that transformers are considered safer?
Transformers are safer because they are isolating your voltage from the mains (even if your transformer is 1:1 and there is no voltage difference).

The reason is the ground connection (please see this article for difference of ground and neutral).

A really good answer with pictures you can find here

To sum it up. If your ciruit is not isolated and you touch a single wire of it the current can flow through your body to ground. If your circuit is isolated by a transformer, the floor you are standing on has no connection to the secondary circuit of your transformer. The voltage potential will be only between the secondary wires of your transformer. So touching a single wire will not let any current flow through your body. Only when you touch 2 positions of your circuit with different potential, current will flow through your body. 
Its considered safer as the chance to accidentally touch 2 positions in your circuit is less then only one!

A voltage divider does not have this effect, as it will not isolate your circuit from ground.