I am so sorry that Rachel was sent home, and I do wish that Simon had chosen her as opposed to leaving it to the public vote because I really like her.
However, as much as I do believe that she was the better singer and should have remained in the competition, I understand why Simon didn't just chose her.
This would have been either the second or third time that she was in the bottom two, and that demonstrates that she is not popular with the public. And obviously, if this is the third time that the public has voted against her, she can't possibly get far in the competition. It just means that they would have eventually voted her out anyway.
Furthermore,if the public doesn't like her, she would not make money in the entertainment industry, because that is all about popularity and likability. And if she has neither, she can't possibly progress.