If Young Paul is still loyal to the uncle, his reasoning for going after Whitey are numerous:

Big Paul delivered drugs for Whitey and Flemmi in the 80s. After going to prison for 6 years, the uncle refused to work for them going forward. This irked Whitey and Stevie. No word how they responded, but based on what we know about them, it was probably a threatening nature.

Big Paul was an enemy of Salemme. Salemme was aligned, at least partially, with Whitey and Stevie at one point or another.

Then there's the fact that Young Paul was railroaded by his own dad, an informant. If that doesn't make you hate informants and the whole program, I'm not sure what will. Plenty of reasons why Young Paul and Geas would take action against Whitey.