Why Not Me received mostly positive reviews from critics following its release. In October 1984,
Billboard took notice of the album's attention to detail and highlighted several tracks in their review: "The meteoric success story of this duo is no accident. It's predicated on exactly the kind of purity, acoustic brilliance and attention to detail that shines here on the sisters' first full album". Music journalist
Robert Christgau gave the album a mostly favorable response, but disliked the production style at times, giving it a "B" rating: "After defying convention by indulging not a single soppy song on their tryout EP, they've flabbed the follow-up several times. And I bet they get even more complacent."
AllMusic's Thom Jurek called the album a "bona fide classic" and praised its "soaring harmonies" as well as the lead vocals from Wynonna Judd. He also noticed a connection between neo-traditional country and classic country from the early 60s, drawing comparisons to
Patsy Cline. Jurek concluded by saying, "Of all their recordings, Why Not Me is their best-known, best-selling, and deservedly so. It's perfect." ==Release and chart performance==