Removing background from an image

I recommend diving into selections and masking so you can make good selections and learn how to see what the mask results will be like for your output.https://helpx.adobe.com/photoshop/using/select-mask.html

Learn how to use the dedicated Select And Mask workspace in Photoshop CC.

You may not be able to see all the details when you select and delete a specific region with the selection tools. Fill the layer with an opaque color using transparent pixel lock. After this control step you can make the necessary cleaning. There is also a very old function. Use the Matting function.

Select the guy with the Quick Selection Tool

After you select him click on the top Select and Mask option

In this panel, you can improve your selection, you have to play with the sliders

Here you can watch tutorials and more information

Learn how to use the dedicated Select And Mask workspace in Photoshop CC.

I hope this works for you

Regards

Eugenio

If I am right... then the issue this person is having the outline around the man.

Am I right?  Is that what you mean?

I'm not sure what you mean by "white washed effect". If you are referring to the white edges around the person's head, then save as PNG 24, not PNG 8. PNG 8.

I'd love to help,  but I would need to see a view of your layers and any other information to see what went wrong. But without seeing the layers, it almost sounds like there's information on the other layer that's still there.  Try clicking on the little eyeball, on the left to the layer to make a layer invisible,  to see which layer that background is on.  If that's not working,  we'll see what to do once we see your PS Workspace

What can you see in the Channels and/or Paths windows.  There may be an erroneous layer that needs deleting.

Please post a meaningful screenshot with the pertinent Panels (Layers for example) visible.

What were the png save settings?

I use the Magic Background Tool

If you mean the Background Eraser Tool I advise against that, the Tool is, in my opinion, unfit for serious work.

You might not have noticed those pixels against the checkerboard background but they may have been there all along,

To check a Layer Mask’s fit one can temporarily apply a Stroke (set to »Outer«) to the Layer.