The rubber membrane surrounding the home button is very thin and tears easily.

Apply mild heat (with an iOpener, heat gun, or hair dryer) to soften the adhesive securing the home button membrane.

Using your fingertip, apply firm, constant pressure on the home button from the front side of the display assembly, until the membrane starts to separate from the front panel.

Do not push the home button all the way through—you only need to get a corner free so that you can pry it free with a spudger.