It is a civilian-clothing "Fashion" button, an imitation of the actual US Army eagle-button.
Reasons:
1- It has a "self-shank" back. No actual US Army eagle-buttons had a self-shank back.
2- As your photo of it next to a quarter shows, it is larger than a US quarter-dollar coin (24mm in diameter). The largest size of actual US Army eagle-button was 23mm. Your button is at least 26mm, so it is not an actual US Army eagle-button.