Why is Abraham Lincoln on the penny facing left while the presidents on the dime nickel and quarter all face right?

Actually, as you can see from the coins in your pocket change Lincoln faces to the right while the others (mostly) face left.

The direction is purely an artistic decision. Each coin's design was created by a different sculptor who in most cases used existing portraits, medals, or other sculptors as their inspiration. In fact, on more recent coins the directions have changed - Jefferson now faces somewhat to the right on the nickel, as does Sacajawea on the Native American dollar. Portraits on coins in the past have also faced different directions as decided by the sculptor.

Regardless of internet conspiracy theories, there's no deeper or more sinister reason - it's just artistic license.