Pixels are being deleted from my selection when I cut and paste it as a new layer?

[YBLee123]

I used to be able to make a selection of the clear part on a glass bottle. Cut the selection, paste it as a new layer and lower the opacity to make it transparent to give it a more realistic look. However, when I try this now it always deletes pixels around the selection leaving a gap between the new and old layers.

If anyone could help me fix this problem it would be greatly appreciated. 

Thanks, 

[Omar.Fathy]

You can use the commands in Select>Modify to edit your selection.
The best way for low quality images is to use the Pen Tool to make the perfect selection.

[Michael Bullo]

Have you tried resetting the Photoshop Preferences? They can be found in the Photoshop menu on a Mac and the Edit menu on Windows. Within the General tab is the button Reset Preferences On Quit.

[Bojan Živković]

However, when I try this now it always deletes pixels around the selection leaving a gap between the new and old layers.

By @YBLee123

Let me guess you have problem with anti-aliasing https://helpx.adobe.com/photoshop/key-concepts/aliasing-anti-aliasing.html. If that is not the case try suggestions above. By the way, judge at 100% view. There are numerous work-arounds like to copy, not to cut content or to use healing brush or to simply enlarge content for single pixel. 

[Omar.Fathy]

Would you provide more screenshots for what you do exactly?!
It is about the way you making selection.