Graph Editor backtracking when i'm trying to slow down and speed up the clip.

Never use the Value Graph to attempt to change your timing. It's only for adjusting the VALUE.

To adjust timing (which Easy Ease is designed to do) you need to be looking at the Speed Graph - you have the value graph open which is not the best way of adjusting the timing.

As an example - here's what a "play forwards then play backwards" with TR looks like in the value Graph. As Rick said this will show the value changing over seconds. Its a bit confusing with TR as you are changing seconds over seconds!

This is what the same thing looks like in the Speed Graph. Here you see the speed displayed. In this example it plays at a continuous speed between the first two KFs, then changes speed and plays at a different, but continous speed between the last two. A continuous, or even speed is denoted by a straight, horizontal line:

Here's the middle keyframe with Easy Ease applied:

Notice that it brings both the incoming speed and the outgoing speed to zero which can be a bit brutal. I'm not a huge fan of Easy Ease so I prefer to use Auto-Bezier to smooth out timing like this:

You can see that you get a much smoother curve by using Auto-Bezier.

I hope this helps :-)

You are editing the value graph.

If you don't want to go backwards in time you should not have any downhill curve.

You are not understanding what you are looking at when you use the Graph Editor for time remapping. Take a careful look at the vertical scale on the left. It is showing you time in seconds. If the value line is horizontal then time stands still. If it goes down like you have made it go down here:

That means time is going backward so the video is reversing.

Most folks have trouble visualizing what is going on in the Graph Editor and most folks do not have a good understanding of how time and frame rate relate to each other. There is no bug here, just a failure to understand what you are looking at. If you want the video to always play forward then the line has to be increasing in value as it moves to the right.