Puzzle Problem Explained

I just need another help from this complicated chess puzzle problem today.

In this position, the opponent king is vulnerable and I played Rg3 to advance to the h-file, but unfortunately, chess.com determined that my solution is incorrect and Re3 is correct. I just don't know why it happened.

I assumed Rg3 is another possible solution to this puzzle. Do anyone agrees? The first to comment below will receive a new random daily challenge!

Just a quick glance, Rg3 allows checks to be thrown in and Re3 prevents that.

Yes, the rook on g1 is protecting the king from checks from the black rooks on the b and c files. So it's best to move the e2 rook to e3, and then swing to h3 and then mate on h8. And black can't stop it. 

No I do not agree.

1. Re3 threatens mate in 2, and black will have to lose his b Rook in order to stop it.

1. Rg3 allows black to play Rb1+ and white can no longer win the b Rook with the mate threat.

Chess is a very deep game. if you thought this puzzle was all about checkmating the black King you are wrong. The puzzle is all about winning a Rook.