If you type in this command:

/execute @a[rym=-0,ry=0] ~ ~ ~ /say Hi

You expect it to test for every player looking at a direction between -0 and 0 and make it say "Hi", but nothing happens.

If you want the command to do it, you have to type in:

/execute @a[rym=-1,ry=0] ~ ~ ~ /say Hi

But even if this is the command you type in, it will also detect players that are looking at -1.0, which is a problem when you only want to test for people looking at -0 and 0.
(In the images below, the "ha" scoreboard objective is a "stat.useItem.minecraft.carrot_on_a_stick" objective, so it will only say "Hi" if i right-click the Carrot on a Stick)