What's the idea behind 1. Rc1?
Black can respond with 1... Rb5! 2. Rb1 Rb3! tying white's rook to the defence of the b-pawn. Black's second move is strong because it prevents the b-pawn from moving which would increase the scope of the white rook. After 2. Rb3! white's rook does not have any moves that do not give up the pawn. White's rook is therefore very passive whereas black's rook is active.
After that white has to try to bring the king to the queenside in order to free the rook from the purely defensive task but then black can generate counterplay on the kingside by advancing his pawns (for example g5+h4+g4 etc.) when the black rook on b3 can actually help to put pressure towards the white's kingside. if black for example manages to exchange all the pawns on the kingside he should have a pretty easy draw.
So the basic problem with 1. Rc1? is that it leaves the rook too passive. Piece activity is very important also in the ending. In fact, the fewer pieces there are on the board, the more important it's to keep the remaining pieces active.
Having said that, defending side often has quite considerable drawing chances in a rook ending so there's no quarantee white would win even with a better move than Rc1 but at least black's defence would be more difficult.
I don't understand why Rc1? is bad? Please help.