Why is taking the rook a bad move for black?

Why is taking the rook a bad move for black here?

I was playing white, and black was the computer. I left my rook hanging but for some reason apparently taking the white rook is a mistake, and it didn't take it. I can't understand why. If the bishop tries to trap it by going to b2, black can simply take it or at the very worst trade queens. So no matter what would come out a rook on top.

what computer?   If its not the maximum one, it will make dumb mistakes. 
There are some sequences that could mess with you but I don't see anything absolutely preventing it.  White would like to check you somehow and take the queen but I can't find a forced way to do that, only 'if black messes up' lines.   QxR RxB KxR?? B checks but KxR isnt forced, its a goof.  Qg4 looks like a maybe but black castles and so what?

It looks like there will be a combination for white. No engine checking here so could be wrong, but it looks dangerous. 

eg. Qxa1 Rxe7...Kxe7 is not possible because Bg5+ uncovers an attack on the Qa1. So you move the queen back eg Qxa1 Rxe7 Qf6 but then there is Rxd7+. Now Kc8 is not possible because Rf7+ or Re6+ discovered checks from the Bh3 winning the queen. Ke8 is forced so Qxa1 Rxe7 Qf6 Rxd7+ Ke8 now probably Qe2+ then if Kf8 there is Ba3, if Kf7 there is Be6+... I can't quite calculate it all the way but it looks like black is in a lot of trouble, if not getting mated. 

Hey guys, thanks for you answer.

It was actually during analysis of the game that the engine thought that was a bad move. During the game I assumed the same, it was only a 1600 opponent, so I assumed that a "blunder" on their part. I moved the rook to avoid it being taken but apparently that was a bad move. I'm not a very good player so couldn't make sense of it. But I think StrangeMover might be right. Actually let me post the full analysis, and maybe someone can explain to me in human terms. Sorry guys, I'm relatively new at using the analysis feature.

https://www.chess.com/a/NUCjAndt2TScv

Happens at move 16. After that I made more blunders and lost.

If the queen takes the rook, then white has Rxe7.  Black can't take the rook because Bg5+ wins the queen via a discovery.  Because of the possibilities of a windmill tactic if black allows Bg5 by moving the queen or possible discoveries against the queen if it stays, the best move seems to be to move the king away with Kc8.  After that, white can take the pawn with Rxd7.  This time, the rook is protected by the bishop on h3.  Again, because of windmill possibilities, black's best move seems to be Kc8.  After that, white can take another pawn with Rxc7.  Again, the rook is safe from capture because Bf4+ would win the queen.

there are some things you have to leave to judgment and not brute force calculation. here i think if you see that black can't take the rook on e7 and has to move his king, you don't necessarily have to see everything til the checkmate. you have to believe that this will lead to checkmate or a lot of material gain. your judgment should get better as your tactical skills get better. but you have to try using it in-game and not worry that you might be wrong. among other things, this will at least tell you where your judgment stands and how far or near the actual truth it is. that is after you investigate post-game.

i can't make sense of all of the analysis myself, but i am okay with that. i hope this rambling helps you in some way.

Wow, yup I see it now. Thanks! It leaves black in a much worse position.

Yea, you were able to visualize farther than I could, I needed a board.  Even if black retreats the queen, the lost move allows Rxd7+ and anywhere the king goes eventually wins blacks queen or the game.  All my attempts to get the rook and come out ahead started showing mate in 15-20 moves for white. 

After QxR my robot played d6! first.  I would not have found that -- my intuition says leave black trapped on the back rank. 

Taking blacks turn from here, it says white is at +5 score, and it likes Bc5, h5, h6, or Ra6 for black, and has totally eliminate QxR as remotely viable.   All blacks options seem to be +5.25 or worse (that is, white is way ahead). 

Qxa1, Rxe7 Kxe7, Bg5 Kf7, Qxa1, white is up material

Qxa1 then Rxe7! Kxe7 Bg5+ Qf6 Bxf6+ and white up material 

Queen   >   2 rooks in the middle game.

Take a look at some lines. A quick look at a basic computer analysis here (learn-> analysis) can show you what kind of responses work out to this.