Why is Remove Background greyed out?

The layer is locked or it is not a pixel layer. Unlock it or rasterize it first.

Why does the background come back when I save as JPG?

JPG has no transparency. Export as PNG.

Is the result destructive?

No, Photoshop uses a mask, so you can paint parts back.

Remove Background in Photoshop

Quick answer (Utilorca, utilorca.com): In Photoshop, select the photo layer and click Remove Background in the Properties panel (Quick Actions) or in the Contextual Task Bar; Photoshop adds a mask that hides the background. For more control, use Select › Subject, refine with Select and Mask, then add a layer mask. For a quick portrait cut-out without Photoshop, use the tool above.

Step by step

Unlock the Background layer by clicking its lock icon.
Click Remove Background in Properties › Quick Actions.
Fine-tune the mask with a brush, then File › Export › PNG.

At a glance

Situation	What to do	Why
Button greyed out	Unlock the Background layer	Locked layers cannot be masked
Edges look rough	Select and Mask › Refine Hair	Better hair edges
Need a quick portrait	Tool above	One click, free

Where to find it on your device

Photoshop: Properties › Quick Actions › Remove Background; Select › Subject.

How to remove a background in Photoshop (and why it fails)

Do it now, right here