Eagle via option 1-16 not shown
The available vias are based on the DRC Layers setup. On the DRC window, go to the Layers tab, and look for the box labelled Setup. This is where you specify how many layers are in your design, but also whether there are any blind or buried vias too.



For a two layer board, Eagle normally uses layer 1 (Top) and layer 16 (Bottom). As such your DRC setup needs to be (1*16). That string means that you have a board using layers 1 and 16 {1 16}, there is a core substrate layer between {*}, and that there are vias that go between these layers {(   )}.

For more complicated boards like 4-layer, you might have a string like (1+2*15+16) which indicates layers 1, 2, 15, and 16 are used, with a core layer separating 2 and 15, then prepreg layers between 1 and 2 and between 15 and 16. Finally the only available via goes from layer 1 to 16, connecting to all in between.



In your case you will instead have the string (1*2) which means that your bottom layer would be on layer 2 rather than 16 (bottom). Simply changing the 2 to be 16 will fix the issue.