Left and right directions make sense if you are routing an edge. The direction depends on whether the router is above the workpiece (routing an edge by hand) or the router is upside-down below the workpiece (routing the edge on a router table).
If you are routing an outside edge by hand with the router bit pointing down and the motor on top, then you want to move the router from left to right along the workpiece edge.
If you are making the same cut with a router table (router upside-down), then you move the workpiece from right to left.
This is very hard to write, but the router bit cutting edge should be rotating against the direction of the cut. The WRONG way would be with the router bit cutting in the direction of the cut, rolling like a tire.
If you move your router in the "wrong" direction, it is called "climb cutting." Climb cutting is considered dangerous. In general, climb cutting is not recommended, and cut quality may be poor. There are a few occasions when experienced woodworkers will use climb cutting in a short segment for special purposes.
If you are cutting a dado in a single pass, then "left and right" direction does not make much sense in that context.
As you move the router for that single pass cut, one side of the router bit will be cutting in the "correct" direction on the "left" side of the dado. At the same time, the other side of the router bit will be "climb cutting" in the "wrong" direction on the "right" side of the dado, possibly yielding a poor quality finish on that "right" side of the dado. Perhaps it is also the cause of chattering or squealing that you heard - from that "right" side.
That's why @TomCT2
recommended using a 1/2 inch router bit with a two-sided guide that's 1/4 inch wider than your router's base. Clamp the guide to your workpiece and run the router against the left edge of the guide "down" the dado towards the stopped end. The left side of the 1/2 inch dado will be clean and good. The right side will not, but it doesn't matter.
Next, move the router across the bottom of the guide (at the end of the dado) to the right side of the guide. That's a 1/4 inch move that will form the bottom of the dado.
Finally, move the router against the right edge of the guide "up" the dado towards the open end on the edge of the workpiece. This will give a smooth cut on the other side of the dado, and remove the bad edge that was created in the first pass.
I hope this helps to answer your questions.