I think it may be true that they may suffer the law better than their competitors. But I think if it was likely that they would benefit absolutely, they'd be in favor of the law, or at least ambivalent, rather than strongly opposed. Don't you?

I personally believe (without any evidence) that they are ambivalent, maybe slightly opposed. However, they needed to oppose in public, otherwise, this would have been a PR disaster:

Publishers: "You steal our content and are unwilling to pay, so we need a law!"

Google: "You're right, please do the law, because it would harm our competitors!"

They could easily couch the statement in such a way that they would appear blameless, if they really wanted to make a positive statement. E.g. "We recognize the critical contribution of publishing companies to our society and want to do our part to ensure the continued existence of a strong publishing industry."

But then why did they not pay voluntarily when publishing companies asked for this prior to lobbying for this law?

Same reason I don't pay extra money to the treasury even though I think my tax rates should be raised.