Rhaegar and Lyanna’s secret marriage (as well as the annulment of Rhaegar’s marriage to Elia Martell, which I still consider a needlessly awful thing to do to his wife and kids) means that Jon is legitimate and male, putting him ahead of Dany in the Targaryen line.
Dany would actually have multiple reasons to want to convince Jon and presumably their allies that the nephew/aunt love connection is all good.
The first and biggest is that, going by the traditions of the Targaryen dynasty, Jon is technically the rightful heir to the Iron Throne over Daenaerys.