What's bad for White in this position is that his structure is already slightly worse (isolated a-pawn), and that Black can worsen it further. White's advanced d-pawn is actually a liability that Black can readily attack by bringing her king forward. The pawn will prove difficult to defend, and at the very least Black can basically force White to accept being saddled with two isolated c-pawns as well by playing
...c6 at some point (when the alternative would be to lose a pawn straightaway on d5).
Is this enough to mean that White is necessarily lost? Probably not (though I certainly wouldn't fancy trying to hold it against a strong engine). But the point is that Black doesn't have similar structural weaknesses, and so she doesn't have the same natural targets to deal with (her doubled pawns aren't nearly the liability that White's are), while White will be forced to keep an eye guarding his queenside. To my mind, this is enough to explain Stockfish preferring Black.
Unfortunately we don't have inline annotations active for the site's PGN viewer, so I will let the verbal explanation already given suffice, and provide just a handful of variations illustrating the points given.
[fen "5k2/pppb1pp1/5p2/3Pn3/4B3/2P2N2/P1P3PP/6K1 w - - 0 1"]
( 1.Nd2 Ke7 2.c4 f5 3.Bd3
( 3.Bf3 Kd6 4.Kf2 Ba4 5.c3 c6 6.dxc6 Bxc6 )
3...c6 4.dxc6 Nxc6 )
1...Ke7 2.Ke3 Kd6 3.Kd4 c5+ $1 4.dxc6
( 4.Ke3 $2 Ng4+ 5.Kd2 f5 6.Bd3 Kxd5 )