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Why do you think Pollux Gallo doesn’t want his brother to be Pope?

My first answer is petty jealousy, but Pollux seems too nice and too cooperative to me, just a concern, he needs deeper investigation.

Probably just an act of jealousy.

I'm hoping it's altruism but we're only halfway through the book so I'm not discounting that he could actually be working to help his brother.

I don’t have enough information about their relationship to hazard a guess.

I also thought he might be helping his brother.

He either knows something we don’t know, or as has been suggested, he’s working to help his brother. No way of knowing, at present.

I think Pollux knows that his brother is not a good man and would therefore not be a good Pope. He knows more about Kastor than he's revealing at this point.